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Tuesday Seminar on Topology
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2016/11/15
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Takuya Sakasai (The University of Tokyo)
Cohomology of the moduli space of graphs and groups of homology cobordisms of surfaces (JAPANESE)
Takuya Sakasai (The University of Tokyo)
Cohomology of the moduli space of graphs and groups of homology cobordisms of surfaces (JAPANESE)
[ Abstract ]
We construct an abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra generated by the fundamental representation of the symplectic group. It gives an alternative proof of the fact first shown by Bartholdi that the top rational homology group of the moduli space of metric graphs of rank 7 is one dimensional. As an application, we construct a non-trivial abelian quotient of the homology cobordism group of a surface of positive genus. This talk is based on joint works with Shigeyuki Morita, Masaaki Suzuki and Gwénaël Massuyeau.
We construct an abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra generated by the fundamental representation of the symplectic group. It gives an alternative proof of the fact first shown by Bartholdi that the top rational homology group of the moduli space of metric graphs of rank 7 is one dimensional. As an application, we construct a non-trivial abelian quotient of the homology cobordism group of a surface of positive genus. This talk is based on joint works with Shigeyuki Morita, Masaaki Suzuki and Gwénaël Massuyeau.
