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Symplectic capacities, unperturbed curves and convex toric domains

Dusa McDuff and Kyler Siegel

Geometry & Topology 28 (2024) 1213–1285
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

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