Topology

2006年4月 -- 7月

[English] [過去のプログラム]

16:30 -- 18:00 数理科学研究科棟(東京大学駒場キャンパス)
Tea: 16:00 -- 16:30 コモンルーム

Last updated June 28, 2006
世話係　
河野俊丈
河澄響矢

4月11日 -- 056号室, 16:30 -- 18:00

Martin Arkowitz (Dartmouth College)

Homotopy actions, cyclic maps and their Eckmann-Hilton duals.

Abstract: We study the homotopy action of a based space A on a based space X. The resulting map A--->X is called cyclic. We classify actions on an H-space which are compatible with the H-structure. In the dual case we study coactions X--->X v B and the resulting cocyclic map X--->B. We relate the cocyclicity of a map to the Lusternik-Schnirelmann category of the map.

4月18日 -- 056号室, 16:30 -- 18:00

Vladimir Turaev (Univ. Louis Pasteur Strasbourg)

Topology of words

Abstract: There is a parallel between words, defined as finite sequences of letters, and curves on surfaces. This allows to treat words as geometric objects and to analyze them using techniques from low-dimensional topology. I will discuss basic ideas in this direction and the resulting topological invariants of words.

4月24日 -- 056号室, 15:00 -- 16:00 モンテシノス教授講演会

Jose Maria Montesinos-Amilibia (Universidad Complutense de Madrid)

Hyperbolic manifolds fibered over S¹ in infinitely many different ways

4月25日 -- 056号室, 16:30 -- 18:00

合田洋 (東京農工大学)

Counting closed orbits and flow lines via Heegaard splittings

Abstract: Let K be a fibred knot in the 3-sphere. It is known that the Alexander polynomial of K is essentially equal to a Lefschetz zeta function obtained from the monodromy map of the fibre structure. In this talk, we discuss the non-fibred knot case. We introduce "monodromy matrix" by making use of Heegaard splitting for sutured manifolds of a knot K, and then observe a method of counting closed orbits and flow lines, which gives the Alexander polynomial of K. This observation is based on works of Donaldson and Mark. (joint work with Hiroshi Matsuda and Andrei Pajitnov)

5月16日 -- 056号室, 17:00 -- 18:30

Laurentiu Maxim (University of Illinois at Chicago)

Fundamental groups of complements to complex hypersurfaces

Abstract: I will survey various Alexander-type invariants of hypersurface complements, with an emphasis on obstructions on the type of groups that can arise as fundamental groups of complements to affine hypersurfaces.

5月23日 -- 056号室, 16:30 -- 18:00

笠川良司 (日本大学理工学部)

On crossed homomorphisms on symplectic mapping class groups

Abstract: We consider a symplectic manifold M. For a relation between Chern classes of M and the cohomology class of the symplectic form, we construct a crossed homomorphism on the symplectomorphism group of M with values in the cohomology group of M. We show an application of it to the flux homomorphism. Then we see that it induces a one on the symplectic mapping class group of M and show a nontrivial example of it.

5月30日 -- 056号室, 16:30 -- 18:00

佐藤隆夫 (東京大学大学院数理科学研究科)

自由群の自己同型群のJohnson準同型の余核について

Abstract: 本講演では，まず次数が2，3の場合に自由群の自己同型群の Johnson準同型の余核の構造を決定する．さらに，次数1の元たちが生成する部分に定義域を制限することで，奇数次のJohnson準同型の全射性に関して新しい障害が得られたことを紹介する．

6月6日 -- 056号室, 16:30 -- 18:00

三好重明 (中央大学理工学部)

Thurston's inequality for a foliation with Reeb components

Abstract: The Euler class of a Reebless foliation or a tight contact structure on a closed 3-manifold satisfies Thurston's inequality, i.e. its (dual) Thurston norm is less than or equal to 1. It should be significant to study Thurston's inequality in both of foliation theory and contact topology. We investigate conditions for a spinnable foliation one of which assures that Thurston's inequality holds and also another of which implies the violation of the inequality.

6月13日 -- 056号室, 16:30 -- 18:00

田中心 (東京大学大学院数理科学研究科)

A note on C1-moves

Abstract: 鎌田氏によりチャートという概念が定義された。これは二次元円板上の有向ラベル付きグラフであり、二次元ブレイドを記述する際に用いられる。彼はチャートに対してC変形と呼ばれる三種類の変形（C1変形、C2変形、C3変形）を定義し、曲面ブレイドの同値類とチャートのC変形同値類の間に一対一対応がある事を示した。カーター氏と斎藤氏は、任意のC1変形は七種類の基本C1変形の列で得られる事を示したが、その証明には曖昧な部分がある事が知られていた。本講演では彼らとは異なるアプローチにより、彼らの主張に対して正しい証明を与える。

6月27日 -- 056号室, 16:30 -- 18:00

Cedric Tarquini (Ecole Nomale Superieure of Lyon)

Lorentzian foliations on 3-manifolds

a joint work with C. Boubel (Ecole Nomale Superieure of Lyon) and P. Mounoud (University of Bordeaux 1 sciences and technologies)

Abstract: The aim of this work is to give a classification of transversely Lorentzian one dimensional foliations on compact manifolds of dimension three. There are the foliations which admit a transverse pseudo-Riemanniann metric of index one. It is the Lorentzian analogue of the better known Riemannian foliations and they still have rigid transverse geometry.

The Riemannian case was listed by Y. Carriere and we will see that the Lorentzian one is very different and much more complicated to classify. The difference comes form the fact that the completness of the transverse structure, which is automatic in the Riemannian case, is a very strong hypothesis for a transverse Lorentzian foliation.

We will give a classification of complete Lorentzian foliations and some examples which are not complete. As a natural corollary of this classification we will list the codimension one timelike geodesically complete totally geodesic foliations of Lorentzian compact three manifolds.

7月4日 -- 056号室, 16:30 -- 18:00

Alexander A. Ivanov (Imperial College (London))

Amalgams: a machinery of the modern theory of finite groups

Abstract

7月11日 -- 056号室, 17:00 -- 18:30

野田健夫 (秋田大学工学資源学部)

全葉層の存在について(浅岡正幸,Emmanuel Dufraineとの共同研究)

Abstract: n次元多様体上のn個の余次元1葉層構造の組で、 n個の葉層構造の接空間の共通部分が各点で0になるものを全葉層と呼ぶ。 3次元の場合においては任意の有向閉多様体上に全葉層が存在することが Hardorpによって示されていた。 3次元多様体上の全葉層をなす各々の葉層構造の接平面場は互いにホモトピックでありオイラー類が0になることが容易に分かるが、逆にオイラー類が0の平面場を与えたときそれを実現する全葉層が存在するかという問題が自然に生じる。本講演ではこの問題に肯定的な解決をあたえる。また、この結果の応用として双接触構造、すなわち横断的に交わる正と負の接触構造の組の存在問題にも触れたい。

7月24日(月） -- 056号室, 16:30 -- 17:30

Boris Hasselblatt (Tufts University)

Invariant foliations in hyperbolic dynamics: Smoothness and smooth equivalence

Abstract: The stable and unstable leaves of a hyperbolic dynamical system are smooth and form a continuous foliation. Smoothness of this foliation sometimes constrains the topological type of the foliation, other times restricts at least the smooth equivalence class of the dynamical system, or for geodesic flows, the type of the underlying manifold. I will present a broad introduction as well as recent work, work in progress, and open problems.