Symplectic embeddings into four‐dimensional concave toric domains

  title={Symplectic embeddings into four‐dimensional concave toric domains},
  author={Keon Choi and Michael Hutchings and Daniel Cristofaro-Gardiner and David Frenkel and Vinicius G. B. Ramos},
  journal={Journal of Topology},
ECH (embedded contact homology) capacities give obstructions to symplectically embedding one symplectic four‐manifold with boundary into another. We compute the ECH capacities of a large family of symplectic four‐manifolds with boundary, called ‘concave toric domains’. Examples include the (nondisjoint) union of two ellipsoids in R4 . We use these calculations to find sharp obstructions to certain symplectic embeddings involving concave toric domains. For example: (1) we calculate the Gromov… 
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Recent progress on symplectic embedding problems in four dimensions
  • M. Hutchings
  • Mathematics
    Proceedings of the National Academy of Sciences
  • 2011
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