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arXiv · 2412.09555

The equivalence of Ekeland-Hofer and equivariant symplectic homology capacities

Jean Gutt·Vinicius G. B. Ramos
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Abstract

In this paper, we prove that the Ekeland-Hofer capacities coincide on all star-shaped domain in $\mathbb{R}^{2n}$ with the equivariant symplectic homology capacities defined by the first author and Hutchings, answering a 35 years old question. Along the way, we prove that given a Hamiltonian $H$, the (equivariant) Floer homology of $H$ is chain-complex isomorphic to the Morse homology of the Hamiltonian action functional.

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Jean Gutt, Vinicius G. B. Ramos. 2024-12-12. The equivalence of Ekeland-Hofer and equivariant symplectic homology capacities. https://arxiv.org/abs/2412.09555

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