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S^1-equivariant index theorems and Morse inequalities on complex manifolds with boundary
时间  Datetime
2018-10-12 13:00 — 14:00 
地点  Venue
Middle Lecture Room
报告人  Speaker
Guokuan Shao
单位  Affiliation
Institute of Mathematics, Academia Sinica
邀请人  Host
王海涛
报告摘要  Abstract

In this talk, we will present new versions of index theorems and Morse inequalities on complex manifolds with boundary. Let M be a relatively compact open subset with connected smooth boundary X of a complex manifold M’. Assume that M admits a holomorphic S^1-action preserving the boundary X and the S^1-action is transversal and CR on X. We claim that the m-th Fourier component of the q-th Dolbeault cohomology group H^q_m(\overline M) is of finite dimension. By using Poisson operator, we prove a reduction theorem which shows that the formulas about H^q_m(\overline M) in our main theorems involve only integrations over X. This talk is based on the joint work with Chin-Yu HSIAO, Rung-Tzung HUANG and Xiaoshan LI.