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

Stephen Yau Tsinghua University Huaiqing Zuo Tsinghua University

Complex Variables and Complex Analysis mathscidoc:1803.08001

SCIENCE CHINA Mathematics, 60, (6), 1129-1136, 2017.6
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 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 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.
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@inproceedings{stephen2017thom-sebastiani,
  title={Thom-Sebastiani properties of Kohn-Rossi cohomology of compact connected strongly pseudoconvex CR manifolds},
  author={Stephen Yau, and Huaiqing Zuo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180307145311957604972},
  booktitle={SCIENCE CHINA Mathematics},
  volume={60},
  number={6},
  pages={1129-1136},
  year={2017},
}
Stephen Yau, and Huaiqing Zuo. Thom-Sebastiani properties of Kohn-Rossi cohomology of compact connected strongly pseudoconvex CR manifolds. 2017. Vol. 60. In SCIENCE CHINA Mathematics. pp.1129-1136. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180307145311957604972.
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