Abstract

Let $X$ be a compact connected CR manifold of dimension $2n+1$, $n\ge 1$. Let $\tilde{X}$ be a paracompact CR manifold with a transversal CR $S^1$-action, such that there is a discrete group $\Gamma$ acting freely on $\tilde{X}$ having $X=\tilde{X}∕\Gamma$. Based on an asymptotic formula for the Fourier components of the heat kernel with respect to the $S^1$-action, we establish the Morse inequalities for Fourier components of reduced $L^2$-Kohn–Rossi cohomology with values in a rigid CR vector bundle over $\tilde{X}$. 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.

Keywords

Mathematical Subject Classification 2010

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