Symplectic capacities from positive S¹-equivariant symplectic homology

2017/07/20 by Jean Gutt, Michael Hutchings · 2 citations
Mathematics · #math.SG

paper · pdf · doi:10.2140/agt.2018.18.3537

published as Algebr. Geom. Topol. 18 (2018) 3537-3600 · 63 pages

arxiv created 2017/07/20 · arxiv updated 2018/10/24

Abstract

We use positive S¹-equivariant symplectic homology to define a sequence of symplectic capacities c_k for star-shaped domains in R²ⁿ. These capacities are conjecturally equal to the Ekeland-Hofer capacities, but they satisfy axioms which allow them to be computed in many more examples. In particular, we give combinatorial formulas for the capacities c_k of any "convex toric domain" or "concave toric domain". As an application, we determine optimal symplectic embeddings of a cube into any convex or concave toric domain. We also extend the capacities c_k to functions of Liouville domains which are almost but not quite symplectic capacities.

Cited by

• The strong Arnol'd chord conjecture for the boundary of a uniformly convex domain in ℝ⁴
• Filtered Symplectic Homology and Closed Reeb Orbits

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