The asymptotics of ECH capacities

• 成果类型: Article
• 署名作者: Cristofaro-Gardiner, Daniel; Hutchings, Michael; Ramos, Vinicius Gripp Barros
• 署名单位: Institute for Advanced Study - USA; University of California System; University of California Berkeley; Nantes Universite
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0510-7
• 发表日期: 2015
• 页码: 187-214
• 关键词: embedded contact homology; gluing pseudoholomorphic curves; seiberg-witten equations; weinstein conjecture; dimensions; PROOF

摘要

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.