The equivalence of Ekeland-Hofer and equivariant symplectic homology capacities
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912153795035136 |
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| author | Gutt, Jean Ramos, Vinicius G. B. |
| author_facet | Gutt, Jean Ramos, Vinicius G. B. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09555 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The equivalence of Ekeland-Hofer and equivariant symplectic homology capacities Gutt, Jean Ramos, Vinicius G. B. Symplectic Geometry 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. |
| title | The equivalence of Ekeland-Hofer and equivariant symplectic homology capacities |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2412.09555 |