Vol. 304, No. 2, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
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
Abstract

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.

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