Volume 18, issue 4 (2018)

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

Volume 24
Issue 7, 3571–4137
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
Symplectic embeddings of four-dimensional polydisks into balls

Katherine Christianson and Jo Nelson

Algebraic & Geometric Topology 18 (2018) 2151–2178
Abstract

We obtain new obstructions to symplectic embeddings of the four-dimensional polydisk P(a,1) into the ball B(c) for 2 a (7 1)(7 2) 2.549, extending work done by Hind and Lisi and by Hutchings. Schlenk’s folding construction permits us to conclude our bound on c is optimal. Our proof makes use of the combinatorial criterion necessary for one “convex toric domain” to symplectically embed into another introduced by Hutchings (2016). We also observe that the computational complexity of this criterion can be reduced from O(2n) to O(n2).

Keywords
symplectic embeddings, embedded contact homology
Mathematical Subject Classification 2010
Primary: 53D05, 53D42
References
Publication
Received: 15 January 2017
Revised: 14 November 2017
Accepted: 8 December 2017
Published: 26 April 2018
Authors
Katherine Christianson
Department of Mathematics
University of California
Berkeley, CA
United States
Jo Nelson
Department of Mathematics
Columbia University
New York, NY
United States
http://www.math.columbia.edu/~nelson/