## Tuesday Seminar on Topology

Seminar information archive ～09/24｜Next seminar｜Future seminars 09/25～

Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
---|---|

Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |

**Seminar information archive**

### 2013/06/25

17:10-18:10 Room #056 (Graduate School of Math. Sci. Bldg.)

Higher-order generalization of Fukaya's Morse homotopy

invariant of 3-manifolds (JAPANESE)

**Tadayuki Watanabe**(Shimane University)Higher-order generalization of Fukaya's Morse homotopy

invariant of 3-manifolds (JAPANESE)

[ Abstract ]

In his article published in 1996, K. Fukaya constructed

a 3-manifold invariant by using Morse homotopy theory. Roughly, his

invariant is defined by considering several Morse functions on a

3-manifold and counting with weights the ways that the theta-graph can

be immersed such that edges follow gradient lines. We generalize his

construction to 3-valent graphs with arbitrary number of loops for

integral homology 3-spheres. I will also discuss extension of our method

to 3-manifolds with positive first Betti numbers.

In his article published in 1996, K. Fukaya constructed

a 3-manifold invariant by using Morse homotopy theory. Roughly, his

invariant is defined by considering several Morse functions on a

3-manifold and counting with weights the ways that the theta-graph can

be immersed such that edges follow gradient lines. We generalize his

construction to 3-valent graphs with arbitrary number of loops for

integral homology 3-spheres. I will also discuss extension of our method

to 3-manifolds with positive first Betti numbers.

### 2013/06/18

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Left-orderable, non-L-space surgeries on knots (JAPANESE)

**Kimihiko Motegi**(Nihon University)Left-orderable, non-L-space surgeries on knots (JAPANESE)

[ Abstract ]

A Dehn surgery is said to be left-orderable

if the resulting manifold of the surgery has the left-orderable fundamental group,

and a Dehn surgery is called an L-space surgery

if the resulting manifold of the surgery is an L-space.

We will focus on left-orderable, non-L-space surgeries on knots in the 3-sphere.

Once we have a knot with left-orderable surgeries,

the ``periodic construction" enables us to provide infinitely many knots with

left-orderable, non-L-space surgeries.

We apply the construction to present infinitely many hyperbolic knots on each

of which every nontrivial surgery is a left-orderable, non-L-space surgery.

This is a joint work with Masakazu Teragaito.

A Dehn surgery is said to be left-orderable

if the resulting manifold of the surgery has the left-orderable fundamental group,

and a Dehn surgery is called an L-space surgery

if the resulting manifold of the surgery is an L-space.

We will focus on left-orderable, non-L-space surgeries on knots in the 3-sphere.

Once we have a knot with left-orderable surgeries,

the ``periodic construction" enables us to provide infinitely many knots with

left-orderable, non-L-space surgeries.

We apply the construction to present infinitely many hyperbolic knots on each

of which every nontrivial surgery is a left-orderable, non-L-space surgery.

This is a joint work with Masakazu Teragaito.

### 2013/06/11

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

On an analogue of Culler-Shalen theory for higher-dimensional

representations

(JAPANESE)

**Takahiro Kitayama**(The University of Tokyo)On an analogue of Culler-Shalen theory for higher-dimensional

representations

(JAPANESE)

[ Abstract ]

Culler and Shalen established a way to construct incompressible surfaces

in a 3-manifold from ideal points of the SL_2-character variety. We

present an analogous theory to construct certain kinds of branched

surfaces from limit points of the SL_n-character variety. Such a

branched surface induces a nontrivial presentation of the fundamental

group as a 2-dimensional complex of groups. This is a joint work with

Takashi Hara (Osaka University).

Culler and Shalen established a way to construct incompressible surfaces

in a 3-manifold from ideal points of the SL_2-character variety. We

present an analogous theory to construct certain kinds of branched

surfaces from limit points of the SL_n-character variety. Such a

branched surface induces a nontrivial presentation of the fundamental

group as a 2-dimensional complex of groups. This is a joint work with

Takashi Hara (Osaka University).

### 2013/06/04

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Low-dimensional linear representations of mapping class groups. (ENGLISH)

**Mustafa Korkmaz**(Middle East Technical University)Low-dimensional linear representations of mapping class groups. (ENGLISH)

[ Abstract ]

For a compact connected orientable surface, the mapping class group

of it is defined as the group of isotopy classes of orientation-preserving

self-diffeomorphisms of S which are identity on the boundary. The action

of the mapping class group on the first homology of the surface

gives rise to the classical 2g-dimensional symplectic representation.

The existence of a faithful linear representation of the mapping class

group is still unknown. In my talk, I will show the following three results;

there is no lower dimensional (complex) linear representation,

up to conjugation the symplectic representation is the unique nontrivial representation in dimension 2g, and there is no faithful linear representation

of the mapping class group in dimensions up to 3g-3. I will also discuss a few applications of these theorems, including some algebraic consequences.

For a compact connected orientable surface, the mapping class group

of it is defined as the group of isotopy classes of orientation-preserving

self-diffeomorphisms of S which are identity on the boundary. The action

of the mapping class group on the first homology of the surface

gives rise to the classical 2g-dimensional symplectic representation.

The existence of a faithful linear representation of the mapping class

group is still unknown. In my talk, I will show the following three results;

there is no lower dimensional (complex) linear representation,

up to conjugation the symplectic representation is the unique nontrivial representation in dimension 2g, and there is no faithful linear representation

of the mapping class group in dimensions up to 3g-3. I will also discuss a few applications of these theorems, including some algebraic consequences.

### 2013/05/21

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

A Heegaard Floer homology for bipartite spatial graphs and its

properties (ENGLISH)

**Yuanyuan Bao**(The University of Tokyo)A Heegaard Floer homology for bipartite spatial graphs and its

properties (ENGLISH)

[ Abstract ]

A spatial graph is a smooth embedding of a graph into a given

3-manifold. We can regard a link as a particular spatial graph.

So it is natural to ask whether it is possible to extend the idea

of link Floer homology to define a Heegaard Floer homology for

spatial graphs. In this talk, we discuss some ideas towards this

question. In particular, we define a Heegaard Floer homology for

bipartite spatial graphs and discuss some further observations

about this construction. We remark that Harvey and O’Donnol

have announced a combinatorial Floer homology for spatial graphs by

considering grid diagrams.

A spatial graph is a smooth embedding of a graph into a given

3-manifold. We can regard a link as a particular spatial graph.

So it is natural to ask whether it is possible to extend the idea

of link Floer homology to define a Heegaard Floer homology for

spatial graphs. In this talk, we discuss some ideas towards this

question. In particular, we define a Heegaard Floer homology for

bipartite spatial graphs and discuss some further observations

about this construction. We remark that Harvey and O’Donnol

have announced a combinatorial Floer homology for spatial graphs by

considering grid diagrams.

### 2013/05/14

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Vanishing cycles and homotopies of wrinkled fibrations (JAPANESE)

**Kenta Hayano**(Osaka University)Vanishing cycles and homotopies of wrinkled fibrations (JAPANESE)

[ Abstract ]

Wrinkled fibrations on closed 4-manifolds are stable

maps to closed surfaces with only indefinite singularities. Such

fibrations and variants of them have been studied for the past few years

to obtain new descriptions of 4-manifolds using mapping class groups.

Vanishing cycles of wrinkled fibrations play a key role in these studies.

In this talk, we will explain how homotopies of wrinkled fibrtions affect

their vanishing cycles. Part of the results in this talk is a joint work

with Stefan Behrens (Max Planck Institute for Mathematics).

Wrinkled fibrations on closed 4-manifolds are stable

maps to closed surfaces with only indefinite singularities. Such

fibrations and variants of them have been studied for the past few years

to obtain new descriptions of 4-manifolds using mapping class groups.

Vanishing cycles of wrinkled fibrations play a key role in these studies.

In this talk, we will explain how homotopies of wrinkled fibrtions affect

their vanishing cycles. Part of the results in this talk is a joint work

with Stefan Behrens (Max Planck Institute for Mathematics).

### 2013/05/07

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Homological intersection in braid group representation and dual

Garside structure (JAPANESE)

**Tetsuya Ito**(RIMS, Kyoto University)Homological intersection in braid group representation and dual

Garside structure (JAPANESE)

[ Abstract ]

One method to construct linear representations of braid groups is to use

an action of braid groups on certain homology of local system coefficient.

Many famous representations, such as Burau or Lawrence-Krammer-Bigelow

representations are constructed in such a way. We show that homological

intersections on such homology groups are closely related to the dual

Garside structure, a remarkable combinatorial structure of braid, and

prove that some representations detects the length of braids in a

surprisingly simple way.

This work is partially joint with Bert Wiest (Univ. Rennes1).

One method to construct linear representations of braid groups is to use

an action of braid groups on certain homology of local system coefficient.

Many famous representations, such as Burau or Lawrence-Krammer-Bigelow

representations are constructed in such a way. We show that homological

intersections on such homology groups are closely related to the dual

Garside structure, a remarkable combinatorial structure of braid, and

prove that some representations detects the length of braids in a

surprisingly simple way.

This work is partially joint with Bert Wiest (Univ. Rennes1).

### 2013/04/30

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Discrete vector fields and fundamental algebraic topology.

(ENGLISH)

**Francis Sergeraert**(L'Institut Fourier, Univ. de Grenoble)Discrete vector fields and fundamental algebraic topology.

(ENGLISH)

[ Abstract ]

Robin Forman invented the notion of Discrete Vector Field in 1997.

A recent common work with Ana Romero allowed us to discover the notion

of Eilenberg-Zilber discrete vector field. Giving the topologist a

totally new understanding of the fundamental tools of combinatorial

algebraic topology: Eilenberg-Zilber theorem, twisted Eilenberg-Zilber

theorem, Serre and Eilenberg-Moore spectral sequences,

Eilenberg-MacLane correspondence between topological and algebraic

classifying spaces. Gives also new efficient algorithms for Algebraic

Topology, considerably improving our computer program Kenzo, devoted

to Constructive Algebraic Topology. The talk is devoted to an

introduction to discrete vector fields, the very simple definition of

the Eilenberg-Zilber vector field, and how it can be used in various

contexts.

Robin Forman invented the notion of Discrete Vector Field in 1997.

A recent common work with Ana Romero allowed us to discover the notion

of Eilenberg-Zilber discrete vector field. Giving the topologist a

totally new understanding of the fundamental tools of combinatorial

algebraic topology: Eilenberg-Zilber theorem, twisted Eilenberg-Zilber

theorem, Serre and Eilenberg-Moore spectral sequences,

Eilenberg-MacLane correspondence between topological and algebraic

classifying spaces. Gives also new efficient algorithms for Algebraic

Topology, considerably improving our computer program Kenzo, devoted

to Constructive Algebraic Topology. The talk is devoted to an

introduction to discrete vector fields, the very simple definition of

the Eilenberg-Zilber vector field, and how it can be used in various

contexts.

### 2013/04/23

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Twisted Novikov homology and jump loci in formal and hyperformal spaces (ENGLISH)

**Andrei Pajitnov**(Univ. de Nantes)Twisted Novikov homology and jump loci in formal and hyperformal spaces (ENGLISH)

[ Abstract ]

Let X be a CW-complex, G its fundamental group, and R a repesentation of G.

Any element of the first cohomology group of X gives rise to an exponential

deformation of R, which can be considered as a curve in the space of

representations. We show that the cohomology of X with local coefficients

corresponding to the generic point of this curve is computable from a spectral

sequence starting from the cohomology of X with R-twisted coefficients. We

compute the differentials of the spectral sequence in terms of Massey products,

and discuss some particular cases arising in Kaehler geometry when the spectral

sequence degenerates. We explain the relation of these invariants and the

twisted Novikov homology. This is a joint work with Toshitake Kohno.

Let X be a CW-complex, G its fundamental group, and R a repesentation of G.

Any element of the first cohomology group of X gives rise to an exponential

deformation of R, which can be considered as a curve in the space of

representations. We show that the cohomology of X with local coefficients

corresponding to the generic point of this curve is computable from a spectral

sequence starting from the cohomology of X with R-twisted coefficients. We

compute the differentials of the spectral sequence in terms of Massey products,

and discuss some particular cases arising in Kaehler geometry when the spectral

sequence degenerates. We explain the relation of these invariants and the

twisted Novikov homology. This is a joint work with Toshitake Kohno.

### 2013/04/09

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Colored HOMFLY Homology and Super-A-polynomial (JAPANESE)

**Hiroyuki Fuji**(The University of Tokyo)Colored HOMFLY Homology and Super-A-polynomial (JAPANESE)

[ Abstract ]

This talk is based on works in collaboration with S. Gukov, M. Stosic,

and P. Sulkowski. We study the colored HOMFLY homology for knots and

its asymptotic behavior. In recent years, the categorification of the

colored HOMFLY polynomial is proposed in term of homological

discussions via spectral sequence and physical discussions via refined

topological string, and these proposals give the same answer

miraculously. In this talk, we consider the asymptotic behavior of the

colored HOMFLY homology \\`a la the generalized volume conjecture, and

discuss the quantum structure of the colored HOMFLY homology for the

complete symmetric representations via the generalized A-polynomial

which we call “super-A-polynomial”.

This talk is based on works in collaboration with S. Gukov, M. Stosic,

and P. Sulkowski. We study the colored HOMFLY homology for knots and

its asymptotic behavior. In recent years, the categorification of the

colored HOMFLY polynomial is proposed in term of homological

discussions via spectral sequence and physical discussions via refined

topological string, and these proposals give the same answer

miraculously. In this talk, we consider the asymptotic behavior of the

colored HOMFLY homology \\`a la the generalized volume conjecture, and

discuss the quantum structure of the colored HOMFLY homology for the

complete symmetric representations via the generalized A-polynomial

which we call “super-A-polynomial”.

### 2013/03/19

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Open book foliation and application to contact topology (ENGLISH)

**Keiko Kawamuro**(University of Iowa)Open book foliation and application to contact topology (ENGLISH)

[ Abstract ]

Open book foliation is a generalization of Birman and Menasco's braid foliation. Any 3-manifold admits open book decompositions. Open book foliation is a singular foliation on an embedded surface, and is define by the intersection of a surface and the pages of the open book decomposition. By Giroux's identification of open books and contact structures one can use open book foliation method to study contact structures. In this talk I define the open book foliation and show some applications to contact topology. This is joint work with Tetsuya Ito (University of British Columbia).

Open book foliation is a generalization of Birman and Menasco's braid foliation. Any 3-manifold admits open book decompositions. Open book foliation is a singular foliation on an embedded surface, and is define by the intersection of a surface and the pages of the open book decomposition. By Giroux's identification of open books and contact structures one can use open book foliation method to study contact structures. In this talk I define the open book foliation and show some applications to contact topology. This is joint work with Tetsuya Ito (University of British Columbia).

### 2013/02/19

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

On the ring of Fricke characters of free groups (JAPANESE)

**Eri Hatakenaka**(Tokyo University of Agriculture and Technology)On the ring of Fricke characters of free groups (JAPANESE)

[ Abstract ]

This is a joint work with Takao Satoh (Tokyo University of Science). We study a descending filtration of the ring of Fricke characters of a free group consisting of ideals on which the automorphism group of the free group naturally acts. Then by using it, we define a descending filtration of the automorphism group of a free group, and investigate a relation between it and the Andreadakis-Johnson filtration.

This is a joint work with Takao Satoh (Tokyo University of Science). We study a descending filtration of the ring of Fricke characters of a free group consisting of ideals on which the automorphism group of the free group naturally acts. Then by using it, we define a descending filtration of the automorphism group of a free group, and investigate a relation between it and the Andreadakis-Johnson filtration.

### 2013/01/22

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

On the autonomous metric of the area preserving diffeomorphism

of the two dimensional disc. (ENGLISH)

**Jarek Kedra**(University of Aberdeen)On the autonomous metric of the area preserving diffeomorphism

of the two dimensional disc. (ENGLISH)

[ Abstract ]

Let D be the open unit disc in the Euclidean plane and let

G:=Diff(D, area) be the group of smooth compactly supported

area-preserving diffeomorphisms of D. A diffeomorphism is called

autonomous if it is the time one map of the flow of a time independent

vector field. Every diffeomorphism in G is a composition of a number

of autonomous diffeomorphisms. The least amount of such

diffeomorphisms defines a norm on G. In the talk I will investigate

geometric properties of such a norm.

In particular I will construct a bi-Lipschitz embedding of the free

abelian group of arbitrary rank to G. I will also show that the space

of homogeneous quasi-morphisms vanishing on all autonomous

diffeomorphisms in G is infinite dimensional.

This is a joint work with Michael Brandenbursky.

Let D be the open unit disc in the Euclidean plane and let

G:=Diff(D, area) be the group of smooth compactly supported

area-preserving diffeomorphisms of D. A diffeomorphism is called

autonomous if it is the time one map of the flow of a time independent

vector field. Every diffeomorphism in G is a composition of a number

of autonomous diffeomorphisms. The least amount of such

diffeomorphisms defines a norm on G. In the talk I will investigate

geometric properties of such a norm.

In particular I will construct a bi-Lipschitz embedding of the free

abelian group of arbitrary rank to G. I will also show that the space

of homogeneous quasi-morphisms vanishing on all autonomous

diffeomorphisms in G is infinite dimensional.

This is a joint work with Michael Brandenbursky.

### 2013/01/21

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

)

Lie foliations transversely modeled on nilpotent Lie

algebras

(JAPANESE)

**Naoki Kato**(The University of Tokyo)

Lie foliations transversely modeled on nilpotent Lie

algebras

(JAPANESE)

[ Abstract ]

To each Lie $\\mathfrak{g}$-foliation, there is an associated subalgebra

$\\mathfrak{h}$ of $\\mathfrak{g}$ with the foliation, which is called the

structure Lie algabra. In this talk, we will explain the inverse problem,

that is, which pair $(\\mathfrak{g},\\mathfrak{h})$ can be realized as a

Lie $\\mathfrak{g}$-foliation with the structure Lie algabra $\\mathfrak{h}

$, under the assumption that $\\mathfrak{g}$ is nilpotent.

To each Lie $\\mathfrak{g}$-foliation, there is an associated subalgebra

$\\mathfrak{h}$ of $\\mathfrak{g}$ with the foliation, which is called the

structure Lie algabra. In this talk, we will explain the inverse problem,

that is, which pair $(\\mathfrak{g},\\mathfrak{h})$ can be realized as a

Lie $\\mathfrak{g}$-foliation with the structure Lie algabra $\\mathfrak{h}

$, under the assumption that $\\mathfrak{g}$ is nilpotent.

### 2013/01/21

17:30-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Quasi-morphisms on the group of area-preserving diffeomorphisms of

the 2-disk

(JAPANESE)

**Tomohiko Ishida**(The University of Tokyo)Quasi-morphisms on the group of area-preserving diffeomorphisms of

the 2-disk

(JAPANESE)

[ Abstract ]

Gambaudo and Ghys constructed linearly independent countably many quasi-

morphisms on the group of area-preserving diffeomorphisms of the 2-disk

from quasi-morphisms on braid groups.

In this talk, we will explain that their construction is injective as a

homomorphism between vector spaces of quasi-morphisms.

If time permits, we introduce an application by Brandenbursky and K\\c{e}

dra.

Gambaudo and Ghys constructed linearly independent countably many quasi-

morphisms on the group of area-preserving diffeomorphisms of the 2-disk

from quasi-morphisms on braid groups.

In this talk, we will explain that their construction is injective as a

homomorphism between vector spaces of quasi-morphisms.

If time permits, we introduce an application by Brandenbursky and K\\c{e}

dra.

### 2012/12/11

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Homotopy-theoretic methods in the study of spaces of knots and links (ENGLISH)

**Ismar Volic**(Wellesley College)Homotopy-theoretic methods in the study of spaces of knots and links (ENGLISH)

[ Abstract ]

I will survey the ways in which some homotopy-theoretic

methods, manifold calculus of functors main among them, have in recent

years been used for extracting information about the topology of

spaces of knots and links. Cosimplicial spaces and operads will also

be featured. I will end with some recent results about spaces of

homotopy string links and in particular about how one can use functor

calculus in combination with configuration space integrals to extract

information about Milnor invariants.

I will survey the ways in which some homotopy-theoretic

methods, manifold calculus of functors main among them, have in recent

years been used for extracting information about the topology of

spaces of knots and links. Cosimplicial spaces and operads will also

be featured. I will end with some recent results about spaces of

homotopy string links and in particular about how one can use functor

calculus in combination with configuration space integrals to extract

information about Milnor invariants.

### 2012/12/04

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Conformal field theory for C2-cofinite vertex algebras (JAPANESE)

**Yoshitake Hashimoto**(Tokyo City University)Conformal field theory for C2-cofinite vertex algebras (JAPANESE)

[ Abstract ]

This is a jount work with Akihiro Tsuchiya (Kavli IPMU).

We consider sheaves of covacua and conformal blocks over parameter spaces of n-pointed Riemann surfaces

for a vertex algebra of which the category of modules is not necessarily semi-simple.

We assume the C2-cofiniteness condition for vertex algebras.

We define "tensor product" of two modules over a C2-cofinite vertex algebra.

This is a jount work with Akihiro Tsuchiya (Kavli IPMU).

We consider sheaves of covacua and conformal blocks over parameter spaces of n-pointed Riemann surfaces

for a vertex algebra of which the category of modules is not necessarily semi-simple.

We assume the C2-cofiniteness condition for vertex algebras.

We define "tensor product" of two modules over a C2-cofinite vertex algebra.

### 2012/11/27

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

On a finite aspect of characteristic classes of foliations (JAPANESE)

**Hiraku Nozawa**(JSPS-IHES fellow)On a finite aspect of characteristic classes of foliations (JAPANESE)

[ Abstract ]

Characteristic classes of foliations are not bounded due to Thurston.

In this talk, we will explain finiteness of characteristic classes for

foliations with certain transverse structures (e.g. transverse

conformally flat structure) and its relation to unboundedness and

rigidity of foliations.

(This talk is based on a joint work with Jesús Antonio

Álvarez López at University of Santiago de Compostela,

which is available as arXiv:1205.3375.)

Characteristic classes of foliations are not bounded due to Thurston.

In this talk, we will explain finiteness of characteristic classes for

foliations with certain transverse structures (e.g. transverse

conformally flat structure) and its relation to unboundedness and

rigidity of foliations.

(This talk is based on a joint work with Jesús Antonio

Álvarez López at University of Santiago de Compostela,

which is available as arXiv:1205.3375.)

### 2012/11/20

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

3 dimensional hyperbolic geometry and cluster algebras (JAPANESE)

**Kentaro Nagao**(Nagoya University)3 dimensional hyperbolic geometry and cluster algebras (JAPANESE)

[ Abstract ]

The cluster algebra was discovered by Fomin-Zelevinsky in 2000.

Recently, the structures of cluster algebras are recovered in

many areas including the theory of quantum groups, low

dimensional topology, discrete integrable systems, Donaldson-Thomas

theory, and string theory and there is dynamic development in the

research on these subjects. In this talk I introduce a relation between

3 dimensional hyperbolic geometry and cluster algebras motivated

by some duality in string theory.

The cluster algebra was discovered by Fomin-Zelevinsky in 2000.

Recently, the structures of cluster algebras are recovered in

many areas including the theory of quantum groups, low

dimensional topology, discrete integrable systems, Donaldson-Thomas

theory, and string theory and there is dynamic development in the

research on these subjects. In this talk I introduce a relation between

3 dimensional hyperbolic geometry and cluster algebras motivated

by some duality in string theory.

### 2012/11/13

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

The virtual fibering theorem and sutured manifold hierarchies (JAPANESE)

**Takahiro Kitayama**(RIMS, Kyoto University,JSPS PD)The virtual fibering theorem and sutured manifold hierarchies (JAPANESE)

[ Abstract ]

In 2007 Agol showed that every irreducible 3-manifold whose fundamental

group is nontrivial and virtually residually finite rationally solvable

(RFRS) is virtually fibered. In the proof he used the theory of

least-weight taut normal surfaces introduced and developed by Oertel and

Tollefson-Wang. We give another proof using complexities of sutured

manifolds. This is a joint work with Stefan Friedl (University of

Cologne).

In 2007 Agol showed that every irreducible 3-manifold whose fundamental

group is nontrivial and virtually residually finite rationally solvable

(RFRS) is virtually fibered. In the proof he used the theory of

least-weight taut normal surfaces introduced and developed by Oertel and

Tollefson-Wang. We give another proof using complexities of sutured

manifolds. This is a joint work with Stefan Friedl (University of

Cologne).

### 2012/11/06

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Galois action on knots (JAPANESE)

**Furusho Hidekazu**(Nagoya University)Galois action on knots (JAPANESE)

[ Abstract ]

I will explain a motivic structure on knots.

Then I will explain that the absolute Galois group of

the rational number field acts non-trivially

on 'the space of knots' in a non-trivial way.

I will explain a motivic structure on knots.

Then I will explain that the absolute Galois group of

the rational number field acts non-trivially

on 'the space of knots' in a non-trivial way.

### 2012/10/30

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Applications of knot theory to molecular biology (JAPANESE)

**Koya Shimokawa**(Saitama University)Applications of knot theory to molecular biology (JAPANESE)

[ Abstract ]

In this talk we discuss applications of knot theory to studies of DNA

and proteins.

Especially we will consider (1)topological characterization of

mechanisms of site-specific recombination systems,

(2)modeling knotted DNA and proteins in confined regions using lattice

knots, and

(3)mechanism of topoisomerases and signed crossing changes.

In this talk we discuss applications of knot theory to studies of DNA

and proteins.

Especially we will consider (1)topological characterization of

mechanisms of site-specific recombination systems,

(2)modeling knotted DNA and proteins in confined regions using lattice

knots, and

(3)mechanism of topoisomerases and signed crossing changes.

### 2012/10/23

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

A geometric approach to the Johnson homomorphisms (JAPANESE)

**Nariya Kawazumi**(The University of Tokyo)A geometric approach to the Johnson homomorphisms (JAPANESE)

[ Abstract ]

We re-construct the Johnson homomorphisms as an embeddig of the Torelli

group

into the completed Goldman-Turaev Lie bialgebra. Then the image is

included in the

kernel of the Turaev cobracket. In the case where the boundary is

connected,

the Turaev cobracket clarifies a geometric meaning of the Morita traces.

Time permitting, we also discuss the case of holed discs.

This talk is based on a joint work with Yusuke Kuno (Tsuda College).

We re-construct the Johnson homomorphisms as an embeddig of the Torelli

group

into the completed Goldman-Turaev Lie bialgebra. Then the image is

included in the

kernel of the Turaev cobracket. In the case where the boundary is

connected,

the Turaev cobracket clarifies a geometric meaning of the Morita traces.

Time permitting, we also discuss the case of holed discs.

This talk is based on a joint work with Yusuke Kuno (Tsuda College).

### 2012/10/16

17:10-18:10 Room #056 (Graduate School of Math. Sci. Bldg.)

Analytic torsion of log-Enriques surfaces (JAPANESE)

**Ken-Ichi Yoshikawa**(Kyoto University)Analytic torsion of log-Enriques surfaces (JAPANESE)

[ Abstract ]

Log-Enriques surfaces are rational surfaces with nowhere vanishing

pluri-canonical forms. We report the recent progress on the computation

of analytic torsion of log-Enriques surfaces.

Log-Enriques surfaces are rational surfaces with nowhere vanishing

pluri-canonical forms. We report the recent progress on the computation

of analytic torsion of log-Enriques surfaces.

### 2012/10/09

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

The growth series of pure Artin groups of dihedral type (JAPANESE)

**Michihiko Fujii**(Kyoto University)The growth series of pure Artin groups of dihedral type (JAPANESE)

[ Abstract ]

In this talk, I consider the kernel of the natural projection from

the Artin group of dihedral type to the corresponding Coxeter group,

that we call a pure Artin group of dihedral type,

and present rational function expressions for both the spherical and

geodesic growth series

of the pure Artin group of dihedral type with respect to a natural

generating set.

Also, I show that their growth rates are Pisot numbers.

This talk is partially based on a joint work with Takao Satoh.

In this talk, I consider the kernel of the natural projection from

the Artin group of dihedral type to the corresponding Coxeter group,

that we call a pure Artin group of dihedral type,

and present rational function expressions for both the spherical and

geodesic growth series

of the pure Artin group of dihedral type with respect to a natural

generating set.

Also, I show that their growth rates are Pisot numbers.

This talk is partially based on a joint work with Takao Satoh.