Tuesday Seminar on Topology

Seminar information archive ~09/27Next seminarFuture seminars 09/28~

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


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


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


16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
佐藤 隆夫 (東京大学大学院数理科学研究科)
[ 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.


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


17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
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.


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


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


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

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