# Symplectic embeddings into four‐dimensional concave toric domains

@article{Choi2013SymplecticEI,
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},
year={2013},
volume={7}
}
• Published 24 October 2013
• Mathematics
• 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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