S1-equivariant index theorems and Morse inequalities on complex manifolds with boundary

讲座时间 Datetime: 

星期四, 2019/06/06 - 从 10:00 到 11:30

地点 Venue: 

海滨红楼6号楼1楼会议室

报告人 Speaker: 

邵国宽 博士

单位 Affiliation: 

中国台湾“中央”研究院

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 in a complex manifold M′. Assume that M admits a holomorphic S1-action preserving the boundary X and the S1-action is transversal and CR on X. We claim that the m-th Fourier component of the q-th Dolbeault cohomology group Hmq (M) is of finite dimension. By using Poisson operator, we prove a reduction theorem which shows that the formulas about Hmq (M) in our main theorems involve only integrations over X. This talk is based on joint work with Chin-Yu HSIAO, Rung-Tzung HUANG and Xiaoshan LI.