# The asymptotics of ECH capacities

@article{CristofaroGardiner2012TheAO, title={The asymptotics of ECH capacities}, author={Daniel Cristofaro-Gardiner and Michael Hutchings and Vinicius G. B. Ramos}, journal={Inventiones mathematicae}, year={2012}, volume={199}, pages={187-214} }

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…

## 56 Citations

An elementary alternative to ECH capacities

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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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In [1], Cristofaro-Gardiner, Hutchings and Ramos proved that embedded contact homology (ECH) capacities of a 4-dimensional symplectic manifold can recover the volume. In particular, a certain…

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Author(s): Cristofaro-Gardiner, Daniel A. | Advisor(s): Hutchings, Michael | Abstract: This dissertation is a collection of four papers involving embedded contact homology (ECH). ECH is a…

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- Mathematics
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Abstract. We prove that, for a C∞-generic contact form λ adapted to a given contact distribution on a closed three-manifold, there exists a sequence of periodic Reeb orbits which is equidistributed…

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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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