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arXiv · 1707.06514

Symplectic capacities from positive S^1-equivariant symplectic homology

Jean Gutt·Michael Hutchings
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Abstract

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.

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Jean Gutt, Michael Hutchings. 2017-07-20. Symplectic capacities from positive S^1-equivariant symplectic homology. https://doi.org/10.2140/agt.2018.18.3537

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