Symplectic embeddings into four-dimensional concave toric domains
Symplectic embeddings into four-dimensional concave toric domains
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DOI：
10.1112/jtopol/jtu008
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发表时间：
2014-12-01
影响因子：
1.1
通讯作者：
Ramos, Vinicius Gripp Barros
中科院分区：
文献类型：
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作者：
Choi, Keon;Cristofaro-Gardiner, Daniel;Ramos, Vinicius Gripp Barros
嵌入切触同调容性是将一个带边界的辛四维流形辛嵌入到另一个带边界的辛四维流形中的障碍。我们计算一个大家庭的辛四流形的边界，称为“凹复曲面域”的ECH能力。例子包括R-4中两个椭球的（不相交）并。我们使用这些计算，以找到尖锐的障碍，某些辛嵌入涉及凹复曲面域。举例来说：（1）我们计算了每个凹复曲面区域的Gromov宽度;（2）我们证明了椭球到椭球和圆柱的并集中的许多包含是“最优的”;（3）我们发现了球填充到椭球和圆柱的某些并集中的尖锐障碍。
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 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.