Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Analytic approach to $S^1$–equivariant Morse inequalities

Mostafa E Zadeh and Reza Moghadasi

Algebraic & Geometric Topology 22 (2022) 3059–3082
Abstract

The cohomology groups of a closed manifold M can be reconstructed using the gradient flow of a Morse–Smale function f : M . A direct result of this construction are Morse inequalities that provide lower bounds for the number of critical points of f in term of Betti numbers of M. Witten showed that these inequalities can be deduced analytically by studying the asymptotic behavior of the deformed Laplacian operator. Adopting Witten’s approach, we provide an analytic proof for the so-called equivariant Morse inequalities when the underlying manifold is acted upon by the Lie group 𝕋 = S1, and the Morse function f is invariant with respect to this action.

PDF Access Denied

We have not been able to recognize your IP address 18.97.14.81 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
equivariant cohomology, Morse inequalities, Witten deformation
Mathematical Subject Classification 2010
Primary: 57R18, 57R99
References
Publication
Received: 8 May 2014
Revised: 22 May 2021
Accepted: 13 September 2021
Published: 30 January 2023
Authors
Mostafa E Zadeh
Department of Mathematical Sciences
Sharif University of Technology
Tehran
Iran
Reza Moghadasi
Department of Mathematical Sciences
Sharif University of Technology
Tehran
Iran