Symplectic embeddings from concave toric domains into convex ones

By Daniel Cristofaro-Gardiner. Journal of differential geometry, 2014

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Embedded contact homology gives a sequence of obstructions to four-dimensional symplectic embeddings, called ECH capacities. In "Symplectic embeddings into four-dimensional concave toric domains", the author, Choi, Frenkel, Hutchings and Ramos computed the ECH capacities of all "concave toric domains", and showed that these give sharp obstructions in several interesting cases. We show that these obstructions are sharp for all symplectic embeddings of concave toric domains into "convex" ones. In an appendix with Choi, we prove a new formula for the ECH capacities of convex toric domains, which shows that they are determined by the ECH capacities of a corresponding collection of balls.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/109384b7ba2680d226f30ee97baeaaa71cf041ca

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Symplectic capacities from positive S1–equivariant symplectic homology (2017, background): “tructions to symplectically embedding a four-dimensional ellipsoid into an ellipsoid [McD11] or polydisk [Hut11b], or more generally a four-dimensional concave toric domain into a convex toric domain [CG14]. In some other situations, such as for some cases of symplectically embedding a four-dimensio”