Volume 18, issue 4 (2018)

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Symplectic embeddings of four-dimensional polydisks into balls

Katherine Christianson and Jo Nelson

Algebraic & Geometric Topology 18 (2018) 2151–2178

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).

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symplectic embeddings, embedded contact homology
Mathematical Subject Classification 2010
Primary: 53D05, 53D42
Received: 15 January 2017
Revised: 14 November 2017
Accepted: 8 December 2017
Published: 26 April 2018
Katherine Christianson
Department of Mathematics
University of California
Berkeley, CA
United States
Jo Nelson
Department of Mathematics
Columbia University
New York, NY
United States