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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（6）
• 页码范围: 1129-1136
• 页数: 8页
• 语种: 英文
• DOI: 10.1007/s11425-016-5125-6

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+1 and Cn+1,respectively.We introduce the ThomSebastiani 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 Cn+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 S1-action.