Symplectic embeddings of four-dimensional polydisks into balls

Christianson, Katherine; Nelson, Jo

doi:10.2140/agt.2018.18.2151

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Symplectic embeddings of four-dimensional polydisks into balls

Katherine Christianson and Jo Nelson

Algebraic & Geometric Topology 18 (2018) 2151–2178

DOI: 10.2140/agt.2018.18.2151

Abstract

We obtain new obstructions to symplectic embeddings of the four-dimensional polydisk $P (a, 1)$ into the ball $B (c)$ for $2 \leq a \leq (\sqrt{7} - 1) ∕ (\sqrt{7} - 2) \approx 2.549$ , 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 $O (2^{n})$ to $O (n^{2})$ .

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/

Volume 18, issue 4 (2018)