トポロジー火曜セミナー

過去の記録 ~02/07次回の予定今後の予定 02/08~

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

過去の記録

2021年12月21日(火)

17:30-18:30   オンライン開催
Lie 群論・表現論セミナーと合同。 参加を希望される場合は、セミナーのウェブページをご覧下さい。
島倉 裕樹 氏 (東北大学)
Classification of holomorphic vertex operator algebras of central charge 24 (JAPANESE)
[ 講演概要 ]
Holomorphic vertex operator algebras are imporant in vertex operator algebra theory. For example, the famous moonshine vertex operator algebra is holomorphic. One of the fundamental problems is to classify holomorphic vertex operator algebras. It is known that holomorphic vertex operator algebras of central charge 8 and 16 are lattice vertex operator algebras. I will talk about recent progress on the classification of holomorphic vertex operator algebras of central charge 24.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年12月07日(火)

17:00-1800   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
佐野 岳人 氏 (東京大学大学院数理科学研究科)
Bar-Natan ホモトピー型の構成 (JAPANESE)
[ 講演概要 ]
2000年に Khovanov は Jones 多項式の圏論化として Khovanov ホモロジー $H_{Kh}$ を構成した. 2014 年に Lipshitz-Sarkar は Khovanov ホモロジーの空間的実現として Khovanov ホモトピー型 $\mathcal{X}_{Kh}$ を構成した. すなわち $\mathcal{X}_{Kh}$ は空間(有限 CW スペクトラム)で, その被約コホモロジー群が Khovanov ホモロジーを復元するものである. Khovanov ホモロジーには Lee ホモロジー, Bar-Natan ホモロジーなどの変種があり, Rasmussen による $s$-不変量など重要な不変量を取り出すこともできる. これらの変種に対してホモトピー型が構成できるかどうかは2020年まで未解決であった. 講演者は 2021年 の論文で,変種の一つである Bar-Natan ホモロジー $H_{BN}$ に対して,その空間的実現である Bar-Natan ホモトピー型 $\mathcal{X}_{BN}$ を構成し, その安定ホモトピー型を決定した. $\mathcal{X}_{BN}$ の構成は $\mathcal{X}_{Kh}$ と同様に Cohen-Jones-Segal が提案したフロー圏による構成法を用いる. 安定ホモトピー型の決定は Lobb らによる「フロー圏における Morse 変形」の手法を用いる. Bar-Natan ホモトピー型を用いた $s$-不変量の空間的精密化は今後の課題である.

https://arxiv.org/abs/2102.07529
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年11月30日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
佐藤 正寿 氏 (東京電機大学)
A non-commutative Reidemeister-Turaev torsion of homology cylinders (JAPANESE)
[ 講演概要 ]
The Reidemeister-Turaev torsion of homology cylinders takes values in the integral group ring of the first homology of a surface. We lift it to a torsion valued in the $K_1$-group of the completed rational group ring of the fundamental group of the surface. We show that it induces a finite type invariant of homology cylinders, and describe the induced map on the graded quotient of the Y-filtration of homology cylinders via the 1-loop part of the LMO functor and the Enomoto-Satoh trace. This talk is based on joint work with Yuta Nozaki and Masaaki Suzuki.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年11月16日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
湯淺 亘 氏 (京都大学数理解析研究所)
Skein and cluster algebras of marked surfaces without punctures for sl(3) (JAPANESE)
[ 講演概要 ]
We consider a skein algebra consisting of sl(3)-webs with the boundary skein relations for a marked surface without punctures. We construct a quantum cluster algebra coming from the moduli space of decorated SL(3)-local systems of the surface inside the skew-field of fractions of the skein algebra. In this talk, we introduce the sticking trick and the cutting trick for sl(3)-webs. The sticking trick expands the boundary-localized skein algebra into the cluster algebra. The cutting trick gives Laurent expressions of "elevation-preserving" webs with positive coefficients in certain clusters. We can also apply these tricks in the case of sp(4). This talk is based on joint works with Tsukasa Ishibashi.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年11月09日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
丸山 修平 氏 (名古屋大学)
The spaces of non-descendible quasimorphisms and bounded characteristic classes (JAPANESE)
[ 講演概要 ]
A quasimorphism is a real-valued function on a group which is a homomorphism up to bounded error. In this talk, we discuss the (non-)descendibility of quasimorphisms. In particular, we consider the space of non-descendible quasimorphisms on universal covering groups and explain its relation to the space of bounded characteristic classes of foliated bundles. This talk is based on a joint work with Morimichi Kawasaki.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年11月02日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
野坂 武史 氏 (東京工業大学)
Meta-nilpotent knot invariants and symplectic automorphism groups of free nilpotent groups (JAPANESE)
[ 講演概要 ]
ファイバー結び目やhomology cylinderというクラスは興味深い幾何・代数的な議論が幾つか展開されてきた。逆に本研究では、ホモロジー3-球面内の任意の結び目をそれらのクラスの様に扱えるように、結び目群のメタ冪零的$p$-局所化を考察する。そのモノドロミーは自由冪零群のシンプレクティック自己同型群の元と見れ、特にその外部自己同型群の共役類からの写像は結び目の不変量を与える。その際にジョンソン準同型の研究が扱える。本講演ではそのモノドロミーの構成と、得られた不変量の研究法を幾つか紹介する。また最近得られた、Fox-ペアリングの視点から考察と結果も紹介する。
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年10月26日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
粕谷 直彦 氏 (北海道大学)
On the strongly pseudoconcave boundary of a compact complex surface (JAPANESE)
[ 講演概要 ]
On the strongly pseudoconvex (resp. pseudoconcave) boundary of a complex surface, the complex
tangency defines a positive (resp. negative) contact structure. Bogomolov and De Oliveira proved
that the boundary contact structure of a strongly pseudoconvex surface is Stein fillable.
Therefore, for a closed contact 3-manifold, Stein fillability and holomorphic fillability are
equivalent. Then what about the boundary of a strongly pseudoconcave surface? We prove that any
closed negative contact 3-manifold can be realized as the boundary of a strongly pseudoconcave
surface. The proof is done by establishing holomorphic handle attaching method to the strongly
pseudoconcave boundary of a complex surface, based on Eliashberg's handlebody construction of Stein
manifolds. This is a joint work with Daniele Zuddas (University of Trieste).
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年10月19日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
四之宮 佳彦 氏 (静岡大学)
Period matrices of some hyperelliptic Riemann surfaces (JAPANESE)
[ 講演概要 ]
In this talk, we give new examples of period matrices of hyperelliptic Riemann surfaces. For generic genus, there were few examples of period matrices. The period matrix of a Riemann surface depends only on the choice of symplectic basis of the first homology group. It is difficult to find a symplectic basis in general. We construct hyperelliptic Riemann surfaces of generic genus from some rectangles and find their symplectic bases. Moreover, we give their algebraic equations. The algebraic equations are of the form $w^2=z(z^2-1)(z^2-a_1^2)(z^2-a_2^2) \cdots (z^2-a_{g-1}^2)$ ($1 < a_1 < a_2 < \cdots < a_{g-1}$). From them, we can calculate period matrices of our Riemann surfaces. We also show that all algebraic curves of this types of equations are obtained by our construction.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年10月12日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
飯田 暢生 氏 (東京大学大学院数理科学研究科)
Seiberg-Witten Floer homotopy and contact structures (JAPANESE)
[ 講演概要 ]
Seiberg-Witten theory has been an efficient tool to study 4-dimensional symplectic and 3-dimensional contact geometry. In this talk, we introduce new homotopical invariants related to these structures using Seiberg-Witten theory and explain their properties and applications. These invariants have two main origins:
1. Kronheimer-Mrowka's invariant for 4-manifold with contact boundary, whose construction is based on Seiberg-Witten equation on 4-manifolds with conical end.
2. Bauer-Furuta and Manolescu's homotopical method called finite dimensional approximation in Seiberg-Witten theory.
This talk includes joint works with Masaki Taniguchi(RIKEN) and Anubhav Mukherjee(Georgia tech).
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年10月05日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
合田 洋 氏 (東京農工大学)
Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds (JAPANESE)
[ 講演概要 ]
We discuss a relationship between the chirality of knots and higher dimensional twisted Alexander polynomials associated with holonomy representations of hyperbolic $3$-cone-manifolds. In particular, we provide a new necessary condition for a knot, that appears in a hyperbolic $3$-cone-manifold of finite volume as a singular set, to be amphicheiral. Moreover, we can detect the chirality of hyperbolic twist knots, according to our criterion, using low-dimensional irreducible representations. (This is a joint work with Takayuki Morifuji.)
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年07月13日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
作間 誠 氏 (大阪市立大学数学研究所)
Homotopy motions of surfaces in 3-manifolds (JAPANESE)
[ 講演概要 ]
We introduce the concept of a homotopy motion of a subset in a manifold, and give a systematic study of homotopy motions of surfaces in closed orientable 3-manifolds. This notion arises from various natural problems in 3-manifold theory such as domination of manifold pairs, homotopical behaviour of simple loops on a Heegaard surface, and monodromies of virtual branched covering surface bundles associated to a Heegaard splitting. This is a joint work with Yuya Koda (arXiv:2011.05766).
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年07月06日(火)

17:30-18:30   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
窪田 陽介 氏 (信州大学)
Codimension 2 transfer map in higher index theory (JAPANESE)
[ 講演概要 ]
The Rosenberg index is a topological invariant taking value in the K-group of the C*-algebra of the fundamental group, which is a strong obstruction for a closed spin manifold to admit a positive scalar curvature (psc) metric. In 2015 Hanke-Pape-Schick proves that, for a nice codimension 2 submanifold N of M, the Rosenberg index of N obstructs to a psc metric on M. This is a far reaching generalization of a classical result of Gromov and Lawson. In this talk I introduce a joint work with T. Schick and its continuation concerned with this `codimension 2 index' obstruction. We construct a map between C*-algebra K-groups, which we call the codimension 2 transfer map, relating the Rosenberg index of M to that of N directly. This shows that Hanke-Pape-Schick's obstruction is dominated by a standard one, the Rosenberg index of M. We also extend our codimension 2 transfer map to secondary index invariants called the higher rho invariant. As a consequence, we obtain some example of psc manifolds are not psc null-cobordant.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年06月29日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
早野 健太 氏 (慶應義塾大学)
Stability of non-proper functions (JAPANESE)
[ 講演概要 ]
In this talk, we will give a sufficient condition for (strong) stability of non-proper functions (with respect to the Whitney topology). As an application, we will give a strongly stable but not infinitesimally stable function. We will further show that any Nash function on the Euclidean space becomes stable after a generic linear perturbation.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年06月22日(火)

17:00-18:30   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
小林 竜馬 氏 (石川工業高等専門学校)
On infinite presentations for the mapping class group of a compact non orientable surface and its twist subgroup (JAPANESE)
[ 講演概要 ]
An infinite presentation for the mapping class group of any compact orientable surface was given by Gervais, and then a simpler one by Luo. Using these results, an infinite presentation for the mapping class group of any compact non orientable surfaces with boundary less than or equal to one was given by Omori (Tokyo University of Science), and then one with boundary more than or equal to two by Omori and the speaker. In this talk, we first introduce an infinite presentation for the twisted subgroup of the mapping class group of any compact non orientable surface. I will also present four simple infinite presentations for the mapping group of any compact non orientable surface, which are an improvement of the one given by Omori and the speaker. This work includes a joint work with Omori.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年06月15日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
佐藤 尚倫 氏 (早稲田大学)
Direct decompositions of groups of piecewise linear homeomorphisms of the unit interval (JAPANESE)
[ 講演概要 ]
In this talk, we consider subgroups of the group PLo(I) of piecewise linear orientation-preserving homeomorphisms of the unit interval I = [0, 1] that are differentiable everywhere except at finitely many real numbers, under the operation of composition. We provide a criterion for any two subgroups of PLo(I) which are direct products of finitely many indecomposable non-commutative groups to be non-isomorphic. As its application we give a necessary and sufficient condition for any two subgroups of the R. Thompson group F that are stabilizers of finite sets of numbers in the interval (0, 1) to be isomorphic.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年06月08日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
松下 尚弘 氏 (琉球大学)
Graphs whose Kronecker coverings are bipartite Kneser graphs (JAPANESE)
[ 講演概要 ]
Kronecker coverings are bipartite double coverings of graphs which are canonically determined. If a graph G is non-bipartite and connected, then there is a unique bipartite double covering of G, and the Kronecker covering of G coincides with it.

In general, there are non-isomorphic graphs although they have the same Kronecker coverings. Therefore, for a given bipartite graph X, it is a natural problem to classify the graphs whose Kronecker coverings are isomorphic to X. Such a classification problem was actually suggested by Imrich and Pisanski, and has been settled in some cases.

In this lecture, we classify the graphs whose Kronecker coverings are bipartite Kneser graphs H(n, k). The Kneser graph K(n, k) is the graph whose vertex set is the family of k-subsets of the n-point set {1, …, n}, and two vertices are adjacent if and only if they are disjoint. The bipartite Kneser graph H(n, k) is the Kronecker covering of K(n, k). We show that there are exactly k graphs whose Kronecker coverings are H(n, k) when n is greater than 2k. Moreover, we determine their automorphism groups and chromatic numbers.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年06月01日(火)

17:30-18:30   オンライン開催
Lie群論・表現論セミナーと合同。 参加を希望される場合は、セミナーのウェブページをご覧下さい。
北川 宜稔 氏 (早稲田大学)
On the discrete decomposability and invariants of representations of real reductive Lie groups (JAPANESE)
[ 講演概要 ]
群の既約表現を部分群に制限したときにどのように振る舞うかを記述する問題を分岐則の問題という。既約表現の制限は一般には既約ではなくなり、ユニタリな場合には直積分で記述される既約分解が存在する。この分解は、ユニタリ作用素のスペクトル分解の一般化とみなすことができ、一般には連続的なスペクトルと離散的なスペクトルが現れる。連続的なスペクトルが現れない場合、つまりユニタリ表現の離散的な直和になっている場合、その表現は離散分解するという。

離散分解する分岐則は技術的に扱いやすいというだけでなく、大きな群の表現の情報から小さい部分群の表現の情報が取り出しやすい状況になっており、以下のような応用が知られている。保型形式から別の保型形式を作り出す Rankin--Cohen ブラケットという作用素は、離散分解する表現から既約表現への絡作用素として得られることが知られており、近年でも多くの一般化が得られている。また、等質空間の L^2 関数の空間の離散スペクトルを別の等質空間のものから構成するという結果にも用いられている。(T. Kobayashi, J. Funct. Anal. ('98))

本講演では、実簡約リー群の既約表現の制限の離散分解性について、小林俊行氏が提唱した離散分解性とG'-許容性の一般論と判定条件(Invent. math. '94, Annals of Math. '98, Invent. math. '98)を踏まえつつ、最近得られた結果を紹介したい。表現の代数的な不変量である随伴多様体、解析的な不変量である wave front set、表現空間の位相、の三つを用いて離散分解性を記述する。
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年05月25日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
足助 太郎 氏 (東京大学大学院数理科学研究科)
On a characteristic class associated with deformations of foliations (JAPANESE)
[ 講演概要 ]
A characteristic class for deformations of foliations called the Fuks-Lodder-Kotschick class (FLK class for short) is discussed. It seems unknown if there is a real foliation with non-trivial FLK class. In this talk, we show some conditions to assure the triviality of the FLK class. On the other hand, we show that the FLK class is easily to be non-trivial for transversely holomorphic foliations. We present an example and give a construction which generalizes it.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年05月18日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
Geoffrey Powell 氏 (CNRS and University of Angers)
On derivations of free algebras over an operad and the generalized divergence (ENGLISH)
[ 講演概要 ]
This talk will first introduce the generalized divergence map from the Lie algebra of derivations of a free algebra over an operad to the trace space of the appropriate associative algebra. This encompasses the Satoh trace (for Lie algebras) and the double divergence of Alekseev, Kawazumi, Kuno and Naef (for associative algebras). The generalized divergence is a Lie 1-cocyle.

One restricts to considering the positive degree subalgebra with respect to the natural grading on the Lie algebra of derivations. The relationship of the positive subalgebra with its subalgebra generated in degree one is of particular interest. For example, this question arises in considering the Johnson morphism in the Lie case.

The talk will outline the structural results obtained by using the generalized divergence. These were inspired by Satoh's study of the kernel of the trace map in the Lie case. A new ingredient is the usage of naturality with respect to the category of free, finite-rank abelian groups and split monomorphisms. This allows global results to be formulated using 'torsion' for functors on this category and extends the usage of naturality with respect to the general linear groups.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年05月11日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
山下 真由子 氏 (京都大学数理解析研究所)
トポロジカルとは限らない invertible QFT の分類問題と, Anderson dual の differential なモデル (JAPANESE)
[ 講演概要 ]
Freed and Hopkins conjectured that the deformation classes of non-topological invertible quantum field theories are classified by a generalized cohomology theory called the Anderson dual of bordism theories. Two of the main difficulty of this problem are the following. First, we do not have the axioms for QFT's. Second, The Anderson dual is defined in an abstract way. In this talk, I will explain the ongoing work to give a new approach to this conjecture, in particular to overcome the second difficulty above. We construct a new, physically motivated model for the Anderson duals. This model is constructed so that it abstracts a certain property of invertible QFT's which physicists believe to hold in general. Actually this construction turns out to be mathematically interesting because of its relation with differential cohomology theories. I will start from basic motivations for the classification problem, reportthe progress of our work and explain future directions. This is the joint work with Yosuke Morita (Kyoto, math) and Kazuya Yonekura (Tohokku, physics).
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2021年04月27日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
栗林 勝彦 氏 (信州大学)
On a singular de Rham complex in diffeology (JAPANESE)
[ 講演概要 ]
Diffeology gives a complete, co-complete, cartesian closed category into which the category of manifolds embeds. In the framework of diffeology, the de Rham complex in the sense of Souriau enables us to develop de Rham calculus. Moreover,Iglesias-Zemmour has been introduced homotopical concepts such as homotopy groups, cubic homology groups and fibrations in diffeology. Thus one might expect `differential homotopy theory'. However, the de Rham theorem does not hold for Souriau's cochain
complex in general. In this talk, I will introduce a singular de Rham complex endowed with an integration map into the singular cochain complex which gives the de Rham theorem for every diffeological space.
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJUpcOCppzwpGd3r_XqdszQ1XN6FvXpNURbj

2021年04月20日(火)

17:00-18:00   オンライン開催
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大鹿 健一 氏 (学習院大学)
Realisation of measured laminations on boundaries of convex cores (JAPANESE)
[ 講演概要 ]
I shall present a generalisation of the theorem by Bonahon-Otal concerning realisation of measured laminations as bending laminations of geometrically finite groups, to general Kleinian surface groups which might be geometrically infinite. Our proof is based on analysis of geometric limits, and is independent of the technique of hyperbolic cone-manifolds employed by Bonahon-Otal. This is joint work with Shinpei Baba (Osaka Univ.).
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJUpcOCppzwpGd3r_XqdszQ1XN6FvXpNURbj

2021年04月13日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
伊藤 哲也 氏 (京都大学)
Quantitative Birman-Menasco theorem and applications to crossing number (JAPANESE)
[ 講演概要 ]
Birman-Menasco proved that there are finitely many knots having a given genus and braid index. We give a quantitative version of Birman-Menasco finiteness theorem; an estimate of the crossing number of knots in terms of genus and braid index. As applications, we give various supporting evidences of various conjectural properties of the crossing number of knots.
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJUpcOCppzwpGd3r_XqdszQ1XN6FvXpNURbj

2021年01月12日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
木村 満晃 氏 (東京大学大学院数理科学研究科)
Bounded cohomology of volume-preserving diffeomorphism groups (JAPANESE)
[ 講演概要 ]
Let M be a complete Riemannian manifold of finite volume. Brandenbursky and Marcinkowski proved that the third bounded cohomology of the volume-preserving diffeomorphism group of M is infinite dimensional when the fundamental group of M is "complicated enough". For example, if M is two-dimensional, the above condition is satisfied if the Euler characteristic is negative. Recently, we have extended this result in the following two directions.

(1) When M is two-dimensional and the Euler characteristic is greater than or equal to zero.
(2) When the volume of M is infinite.

In this talk, we will mainly discuss (1). The key idea is to use the fundamental group of the configuration space of M (i.e., the braid group), rather than the fundamental group of M. If time permits, we will also explain (2). For this extension, we introduce the notion of "norm controlled cohomology".
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2020年12月15日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
金 英子 氏 (大阪大学)
Braids, triangles and Lissajous curve (JAPANESE)
[ 講演概要 ]
The purpose of this talk is to introduce Lissajous 3-braids. Suppose we have a closed curve on the plane, and we consider the periodic motion of n points along the closed curve. If the motion is collision-free, then we get a braid obtained from the trajectory of the set of n points in question. In this talk, we consider 3-braids coming from the periodic motion of 3 points on Lissajous curves. We classify Lissajous 3-braids and present a parametrization in terms of natural numbers together with slopes. We also discuss some properties of pseudo-Anosov stretch factors for Lissajous 3-braids. The main tool is the shape sphere --- the configuration space of the oriented similarity classes of triangles. This is a joint work with Hiroaki Nakamura and Hiroyuki Ogawa.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

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