Symplectic capacities from positive S1–equivariant symplectic homology

By Jean Gutt, Michael Hutchings. Algebraic and Geometric Topology, 2017

81 citations recorded by the source corpus.

We use positive S^1-equivariant symplectic homology to define a sequence of symplectic capacities c_k for star-shaped domains in R^{2n}. 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/adfda6af9a063fb0a71f295ce9b0c8d831bc4619

How researchers see this paper

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In Geometry and Topology

1. F. Schlenk
2. Michael Usher
3. Michael Hutchings
4. D. Mcduff

In Mathematical Physics

1. F. Schlenk
2. Michael Usher
3. Michael Hutchings

Citations in the corpus

• Symplectic embedding problems, old and new (2017, background): “The proof of Theorem 4.5 follows from the recent result of Gutt and Hutchings [52] that the cube {z ∈ C2N+1 | |zk| r for all k} symplectically embeds into ZN N (R) only for r R.”