Volume 25, issue 2 (2021)

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

Volume 28
Issue 7, 3001–3510
Issue 6, 2483–2999
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Mayer–Vietoris property for relative symplectic cohomology

Umut Varolgunes

Geometry & Topology 25 (2021) 547–642
Abstract

We construct a Hamiltonian Floer theory-based invariant called relative symplectic cohomology, which assigns a module over the Novikov ring to compact subsets of closed symplectic manifolds. We show the existence of restriction maps, and prove some basic properties. Our main contribution is to identify natural geometric conditions in which relative symplectic cohomology of two subsets satisfies the Mayer–Vietoris property. These conditions involve certain integrability assumptions involving geometric objects called barriers — roughly, a 1–parameter family of rank 2 coisotropic submanifolds. The proof uses a deformation argument in which the topological energy zero (ie constant) Floer solutions are the main actors.

Keywords
Floer theory, involutive systems, descent
Mathematical Subject Classification 2010
Primary: 53D40
Secondary: 53D37, 81S10
References
Publication
Received: 2 June 2018
Revised: 21 February 2020
Accepted: 13 May 2020
Published: 27 April 2021
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, Mark Gross
Authors
Umut Varolgunes
Department of Mathematics
Stanford University
Stanford, CA
United States