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Tuesday Seminar on Topology
Seminar information archive ～04/22｜Next seminar｜Future seminars 04/23～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2009/10/13
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
笹平 裕史 (東京大学大学院数理科学研究科)
Instanton Floer homology for lens spaces
笹平 裕史 (東京大学大学院数理科学研究科)
Instanton Floer homology for lens spaces
[ Abstract ]
Let Y be an oriented closed 3-manifold and P be an SU(2)-bundle on Y. Under a certain condition, instanton Floer homology for Y can be defined as the Morse homology of the Chern-Simons functional. The condition is that all flat connections on P are irreducible. When there is a reducible flat connection on P, instanton Floer homology is not defined in general.
Since the fundamental group of a lens sapce is commutative, all flat connections on the lens space are reducible. In this talk I will introduce instanton Floer homology for lens spaces. I also show calculations for some lens spaces.
Let Y be an oriented closed 3-manifold and P be an SU(2)-bundle on Y. Under a certain condition, instanton Floer homology for Y can be defined as the Morse homology of the Chern-Simons functional. The condition is that all flat connections on P are irreducible. When there is a reducible flat connection on P, instanton Floer homology is not defined in general.
Since the fundamental group of a lens sapce is commutative, all flat connections on the lens space are reducible. In this talk I will introduce instanton Floer homology for lens spaces. I also show calculations for some lens spaces.
