Thom-Sebastiani properties of Kohn-Rossi cohomology of compact connected strongly pseudoconvex CR manifolds

作     者：YAU Stephen S. T ZUO HuaiQing 

作者机构：Department of Mathematical Sciences Tsinghua University Beijing 100084 China Yau Mathematical Sciences Center Tsinghua University Beijing 100084 China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2017年第60卷第6期

页      面：1129-1136页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11531007 and 11401335) Start-Up Fund from Tsinghua University and Tsinghua University Initiative Scientific Research Program 

主　　题：CR manifold Kohn-Rossi cohomology isolated singularity 

摘      要：Let X1 and X2 be two compact connected strongly pseudoconvex embeddable Cauchy-Riemann （CR） manifolds of dimensions 2m - 1 and 2n - 1 in Cm＋l and Cn＋l, respectively. We introduce the Thom- Sebastiani sum X = X1 X2 which is a new compact connected strongly pseudoconvex embeddable CR manifold of dimension 2m＋2n＋ 1 in Cm＋n＋2. Thus the set of all codimension 3 strongly pseudoconvex compact connected CR manifolds in C^n＋1 for all n ≥ 2 forms a semigroup. X is said to be an irreducible element in this semigroup if X cannot be written in the form X1 X2. It is a natural question to determine when X is an irreducible CR manifold. We use Kohn-Rossi cohomology groups to give a necessary condition of the above question. Explicitly, we show that if X = X1 X2, then the Kohn-Rossi cohomology of the X is the product of those Kohn-Rossi cohomology coming from X1 and X2 provided that X2 admits a transversal holomorphic Sl-action.