$S^1$-equivariant index theorems and Morse inequalities on complex manifolds with boundary

题目:$S^1$-equivariant index theorems and Morse inequalities on complex manifolds with boundary

摘要: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.

报告人:邵国宽,台湾中研院数学所

报告时间:2018.9.17(周一),下午15:00-16:00

报告地点:知新楼B924

邵国宽博士简介:邵国宽博士,台湾中研院数学所博士后。2016年在巴黎第十一大学取得基础数学博士学位。研究方向为多复变、复几何与CR几何,在Trans. Amer. Math. Soc., J. Geom. Anal., Math. Z.等期刊发表论文。

邀请人:扈培础