## トポロジー火曜セミナー

開催情報 火曜日　17:00～18:30　数理科学研究科棟(駒場) 056号室 河野 俊丈, 河澄 響矢, 北山 貴裕, 逆井卓也 http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html Tea: 16:30 - 17:00 コモンルーム

### 2013年10月01日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

The geography problem of Lefschetz fibrations (JAPANESE)
[ 講演概要 ]
To consider holomorphic fibrations complex surfaces over complex curves
and Lefschetz fibrations over surfaces is one method for the study of
complex surfaces of general type and symplectic 4-manifods, respectively.
In this talk, by comparing the geography problem of relatively minimal
holomorphic fibrations with that of relatively minimal Lefschetz
fibrations (i.e., the characterization of pairs $(x,y)$ of certain
invariants $x$ and $y$ corresponding to relatively minimal holomorphic
fibrations and relatively minimal Lefschetz fibrations), we observe the
difference between complex surfaces of general type and symplectic
4-manifolds. In particular, we construct Lefschetz fibrations violating
the slope inequality" which holds for any relatively minimal holomorphic
fibrations.

### 2013年07月16日(火)

17:10-18:10   数理科学研究科棟(駒場) 056号室
Tea: 16:50 - 17:10 コモンルーム

[ 講演概要 ]

### 2013年07月09日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Ryan Budney 氏 (University of Victoria)
Smooth 3-manifolds in the 4-sphere (ENGLISH)
[ 講演概要 ]
Everyone who has studied topology knows the compact 2-manifolds that embed in the 3-sphere. One dimension up, the problem of which smooth 3-manifolds embed in the 4-sphere turns out to be much more involved with a handful of partial answers. I will describe what is known at the present moment.

### 2013年06月25日(火)

17:10-18:10   数理科学研究科棟(駒場) 056号室
Tea: 16:50 - 17:10 コモンルーム

Higher-order generalization of Fukaya's Morse homotopy
invariant of 3-manifolds (JAPANESE)
[ 講演概要 ]
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
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年06月18日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

Left-orderable, non-L-space surgeries on knots (JAPANESE)
[ 講演概要 ]
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年06月11日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

On an analogue of Culler-Shalen theory for higher-dimensional
representations
(JAPANESE)
[ 講演概要 ]
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年06月04日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Mustafa Korkmaz 氏 (Middle East Technical University)
Low-dimensional linear representations of mapping class groups. (ENGLISH)
[ 講演概要 ]
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年05月21日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Yuanyuan Bao 氏 (東京大学大学院数理科学研究科)
A Heegaard Floer homology for bipartite spatial graphs and its
properties (ENGLISH)
[ 講演概要 ]
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
have announced a combinatorial Floer homology for spatial graphs by
considering grid diagrams.

### 2013年05月14日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

Vanishing cycles and homotopies of wrinkled fibrations (JAPANESE)
[ 講演概要 ]
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年05月07日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

Homological intersection in braid group representation and dual
Garside structure (JAPANESE)
[ 講演概要 ]
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年04月30日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Francis Sergeraert 氏 (L'Institut Fourier, Univ. de Grenoble)
Discrete vector fields and fundamental algebraic topology.
(ENGLISH)
[ 講演概要 ]
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年04月23日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Andrei Pajitnov 氏 (Univ. de Nantes)
Twisted Novikov homology and jump loci in formal and hyperformal spaces (ENGLISH)
[ 講演概要 ]
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年04月09日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

[ 講演概要 ]

### 2013年03月19日(火)

16:30-18:00   数理科学研究科棟(駒場) 002号室
Tea: 16:00 - 16:30 コモンルーム

Open book foliation and application to contact topology (ENGLISH)
[ 講演概要 ]
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年02月19日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

On the ring of Fricke characters of free groups (JAPANESE)
[ 講演概要 ]
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年01月22日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Jarek Kedra 氏 (University of Aberdeen)
On the autonomous metric of the area preserving diffeomorphism
of the two dimensional disc. (ENGLISH)
[ 講演概要 ]
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年01月21日(月)

16:30-17:30   数理科学研究科棟(駒場) 002号室

ベキ零リー環を横断構造に持つリー葉層構造について (JAPANESE)
[ 講演概要 ]
リー$\\mathfrak{g}$-葉層構造が与えられたとき,それに付随した構造リー環と呼
ばれる$\\mathfrak{g}$の部分リー環$\\mathfrak{h}$が定まる.本講演ではその逆,
すなわち,リー環$\\mathfrak{g}$とその部分リー環$\\mathfrak{h}$が与えられた
とき構造リー環が$\\mathfrak{h}$となるリー$\\mathfrak{g}$-葉層構造が存在す
るかという問題についてて,$\\mathfrak{g}$がベキ零リー環の場合に説明をする.

### 2013年01月21日(月)

17:30-18:30   数理科学研究科棟(駒場) 002号室

Quasi-morphisms on the group of area-preserving diffeomorphisms of
the 2-disk
(JAPANESE)
[ 講演概要 ]
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年12月11日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Ismar Volic 氏 (Wellesley College)
Homotopy-theoretic methods in the study of spaces of knots and links (ENGLISH)
[ 講演概要 ]
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
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

### 2012年12月04日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

Conformal field theory for C2-cofinite vertex algebras (JAPANESE)
[ 講演概要 ]
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年11月27日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

[ 講演概要 ]
Thurstonの例により、葉層構造の二次特性類は有界でないことが知られている。本講演では、横断的な共形平坦構造などを持つ葉層構造に対しては(例外的な場合を除き)二次特性類が有限性を持つことを、非有界性や葉層構造の剛性との関連と共に説明する。
(本講演はSantiago de Compostela大学のJesús Antonio Álvarez
López氏との共同研究 arXiv:1205.3375に基づく。)

### 2012年11月20日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

3次元双曲幾何と団代数 (JAPANESE)
[ 講演概要 ]
クラスター代数は2000年にFomin-Zelevinskyによって発見された代数系である.

### 2012年11月13日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

The virtual fibering theorem and sutured manifold hierarchies (JAPANESE)
[ 講演概要 ]
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年11月06日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

[ 講演概要 ]

その後、有理数体の絶対ガロア群が'結び目全体が張る空間'に

### 2012年10月30日(火)

16:30-18:00   数理科学研究科棟(駒場) 126号室
Tea: 16:00 - 16:30 コモンルーム

Applications of knot theory to molecular biology (JAPANESE)
[ 講演概要 ]
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.