Symplectic embeddings into disk cotangent bundles

Abstract

In this paper, we compute the embedded contact homology (ECH) capacities of the disk cotangent bundles $D^{\ast }{S}^2$ and $D^{\ast }\mathbb{R}{P}^2$. We also find sharp symplectic embeddings into these domains. In particular, we compute their Gromov widths. In order to do that, we explicitly calculate the ECH chain complexes of $S^{\ast }{S}^2$ and $S^{\ast }\mathbb{R}{P}^2$ using a direct limit argument on the action inspired by Bourgeois's Morse-Bott approach and ideas from Nelson-Weiler's work on the ECH of prequantization bundles. Moreover, we use integrable systems techniques to find explicit symplectic embeddings. In particular, we prove that the disk cotangent bundles of a hemisphere and of a punctured sphere are symplectomorphic to an open ball and a symplectic bidisk, respectively.

arXiv comment35 pages

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Cited by in corpus (3)

• An elementary alternative to ECH capacities
• Symplectic capacities of disc cotangent bundles of flat tori
• Magnetic billiards and the Hofer-Zehnder capacity of disk tangent bundles of lens spaces