トポロジー火曜セミナー

過去の記録 ~05/22次回の予定今後の予定 05/23~

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

過去の記録

2006年05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
笠川 良司 氏 (日本大学理工学部)
On crossed homomorphisms on symplectic mapping class groups
[ 講演概要 ]
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.

2006年05月16日(火)

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム
Laurentiu Maxim 氏 (University of Illinois at Chicago)
Fundamental groups of complements to complex hypersurfaces
[ 講演概要 ]
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.

2006年04月25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
合田 洋 氏 (東京農工大学)
Counting closed orbits and flow lines via Heegaard splittings
[ 講演概要 ]
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)

2006年04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
Vladimir Turaev 氏 (Univ. Louis Pasteur Strasbourg)
Topology of words
[ 講演概要 ]
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.

2006年04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
Martin Arkowitz 氏 (Dartmouth College)
Homotopy actions, cyclic maps and their Eckmann-Hilton duals.
[ 講演概要 ]
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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