Symplectic embeddings into fourdimensional concave toric domains
Abstract
ECH capacities give obstructions to symplectically embedding one symplectic fourmanifold with boundary into another. We compute the ECH capacities of a large family of symplectic fourmanifolds with boundary, called "concave toric domains". Examples include the (nondisjoint) union of two ellipsoids in $\mathbb{R}^4$. We use these calculations to find sharp obstructions to certain symplectic embeddings involving concave toric domains. For example: (1) we calculate the Gromov width of every concave toric domain; (2) we show that many inclusions of an ellipsoid into the union of an ellipsoid and a cylinder are "optimal"; and (3) we find a sharp obstruction to ball packings into certain unions of an ellipsoid and a cylinder.
 Publication:

arXiv eprints
 Pub Date:
 October 2013
 arXiv:
 arXiv:1310.6647
 Bibcode:
 2013arXiv1310.6647C
 Keywords:

 Mathematics  Symplectic Geometry
 EPrint:
 31 pages, 2 figures