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Tuesday Seminar on Topology
Seminar information archive ～03/25｜Next seminar｜Future seminars 03/26～
| Date, time & place | Tuesday 16:00 - 17:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | IKE Yuichi, KONNO Hokuto, SAKASAI Takuya |
2007/12/04
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
今野 宏 (東京大学大学院数理科学研究科)
Morse theory for abelian hyperkahler quotients
今野 宏 (東京大学大学院数理科学研究科)
Morse theory for abelian hyperkahler quotients
[ Abstract ]
In 1980's Kirwan computed Betti numbers of symplectic quotients by using Morse theory. In this talk, we develop this method to hyperkahler quotients by abelian Lie groups. In this method, many computations are much more simplified in the case of hyperkahler quotients than the case of symplectic quotients. As a result we compute not only the Betti numbers, but also the cohomology rings of abelian hyperkahler quotients.
In 1980's Kirwan computed Betti numbers of symplectic quotients by using Morse theory. In this talk, we develop this method to hyperkahler quotients by abelian Lie groups. In this method, many computations are much more simplified in the case of hyperkahler quotients than the case of symplectic quotients. As a result we compute not only the Betti numbers, but also the cohomology rings of abelian hyperkahler quotients.
