# 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} }

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…

## 42 Citations

Symplectic embeddings from concave toric domains into convex ones

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- 2019

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",…

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ECH (embedded contact homology) capacities give obstructions to symplectically embedding one four-dimensional symplectic manifold with boundary into another. These obstructions are known to be sharp…

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In this paper, we compute the embedded contact homology (ECH) capacities of the disk cotangent bundles D∗S2 and D∗RP 2. We also find sharp symplectic embeddings into these domains. In particular, we…

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The ECH capacities are a sequence of numerical invariants of symplectic four-manifolds which give (sometimes sharp) obstructions to symplectic embeddings. These capacities are defined using embedded…

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- 2017

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The ECH capacities are a sequence of real numbers associated to any symplectic four-manifold, which are monotone with respect to symplectic embeddings. It is known that for a compact star-shaped…

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