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
Symplectic capacities, unperturbed curves and convex toric domains

Dusa McDuff and Kyler Siegel
Geometry & Topology 28 (2024) 1213–1285
DOI: 10.2140/gt.2024.28.1213
Abstract

We use explicit pseudoholomorphic curve techniques (without virtual perturbations) to define a sequence of symplectic capacities analogous to those defined recently by the second author using symplectic field theory. We then compute these capacities for all four-dimensional convex toric domains. This gives various new obstructions to stabilized symplectic embedding problems, which are sometimes sharp.

Keywords
symplectic capacities, symplectic embeddings, stabilized symplectic embedding problem, toric domains, obstruction bundle gluing, lattice point counts
Mathematical Subject Classification
Primary: 53D35, 57K43
References
Publication
Received: 31 October 2021
Revised: 17 July 2022
Accepted: 14 August 2022
Published: 10 May 2024
Proposed: Leonid Polterovich
Seconded: Paul Seidel, David Fisher
Authors
Dusa McDuff
Mathematics Department
Columbia University
New York, NY
United States
Kyler Siegel
Department of Mathematics
University of Southern California
Los Angeles, CA
United States
© 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

Open Access made possible by participating institutions via Subscribe to Open.