The asymptotics of ECH capacities
The asymptotics of ECH capacities
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DOI：
10.1007/s00222-014-0510-7
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发表时间：
2015-01-01
影响因子：
3.1
通讯作者：
Ramos, Vinicius Gripp Barros
中科院分区：
文献类型：
--
作者：
Cristofaro-Gardiner, Daniel;Hutchings, Michael;Ramos, Vinicius Gripp Barros
在前一篇文章中，第二作者利用切触三维流形的嵌入切触同调（ECH）定义了四维辛流形的ECH容量。本文证明了对于所有ECH容量有限的四维Liouville域，ECH容量的渐近性恢复到辛体积。这是从一个更一般的定理有关的体积接触三流形的渐近量的辛行动需要代表某些类的ECH。后一个定理被第一和第二作者用来证明闭三流形上的每个接触形式至少有两个嵌入的Reeb轨道。
In a previous paper, the second author used embedded contact homology (ECH) of contact three-manifolds to define "ECH capacities" of four-dimensional symplectic manifolds. In the present paper we prove that for a four-dimensional Liouville domain with all ECH capacities finite, the asymptotics of the ECH capacities recover the symplectic volume. This follows from a more general theorem relating the volume of a contact three-manifold to the asymptotics of the amount of symplectic action needed to represent certain classes in ECH. The latter theorem was used by the first and second authors to show that every contact form on a closed three-manifold has at least two embedded Reeb orbits.