Higher symplectic capacities

Abstract

We construct new families of symplectic capacities indexed by certain symmetric polynomials, defined using rational symplectic field theory. In particular, we introduce a sequence of capacities based on an L-infinity structure on linearized contact homology and rational curve counts with local tangency constraints. We prove various structural properties of these capacities and give some preliminary computations which show that they give state of the art symplectic embedding obstructions in basic examples.

v4: substantial expository revisions, especially in the introduction

References in corpus (8)

• Symplectic embeddings of polydisks
• On Symplectic Sum Formulas in Gromov-Witten Theory
• Cyclic homology, $S^1$-equivariant Floer cohomology, and Calabi-Yau structures
• Counting curves with local tangency constraints
• Holomorphic curves in the presence of holomorphic hypersurface foliations
• Symplectic capacities, unperturbed curves, and convex toric domains
• Lectures on Polyfolds and Symplectic Field Theory
• The stabilized symplectic embedding problem for polydiscs

Cited by in corpus (6)

• Symplectic capacities, unperturbed curves, and convex toric domains
• On the embedding complexity of Liouville manifolds
• ECH embedding obstructions for rational surfaces
• Lattice Formulas For Rational SFT Capacities
• Higher Symplectic Capacities and the Stabilized Embedding Problem for Integral Ellipsoids
• Computing Reeb dynamics on 4d convex polytopes