Vol. 304, No. 2, 2020

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Morse inequalities for Fourier components of Kohn–Rossi cohomology of CR covering manifolds with $S^1$-action

Rung-Tzung Huang and Guokuan Shao

Vol. 304 (2020), No. 2, 439–462

Let X be a compact connected CR manifold of dimension 2n + 1, n 1. Let X˜ be a paracompact CR manifold with a transversal CR S1-action, such that there is a discrete group Γ acting freely on X˜ having X = X˜Γ. Based on an asymptotic formula for the Fourier components of the heat kernel with respect to the S1-action, we establish the Morse inequalities for Fourier components of reduced L2-Kohn–Rossi cohomology with values in a rigid CR vector bundle over X˜. As a corollary, we obtain the Morse inequalities for Fourier components of Kohn–Rossi cohomology on X which were obtained by Hsiao and Li (2016) by using Szegő kernel method.

Kohn–Rossi cohomology, heat kernel, CR manifold
Mathematical Subject Classification 2010
Primary: 32V20
Secondary: 58J35
Received: 13 September 2018
Revised: 2 September 2019
Accepted: 3 September 2019
Published: 12 February 2020
Rung-Tzung Huang
Department of Mathematics
National Central University
Guokuan Shao
School of Mathematics (Zhuhai)
Sun Yat-sen University
Zhuhai, Guangdong