Equivariant Floer homology is isomorphic to reduced Floer homology
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908350603591680 |
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| author | Christ, Julio Sampietro |
| author_facet | Christ, Julio Sampietro |
| contents | Given a symplectic manifold equipped with a Hamiltonian $G$-action and two $G$-invariant Lagrangians, we lift the construction of equivariant Lagrangian Floer homology of G.\@~Cazassus to the Novikov ring by constructing a ``quantum'' model in the vein of Biran and Cornea and Schmäschke. Using this refinement, we prove Cazassus' conjecture that, if the action on the zero-level of the moment map is free, then equivariant Floer homology agrees with the Floer homology of the Marsden-Weinstein reduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02647 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant Floer homology is isomorphic to reduced Floer homology Christ, Julio Sampietro Symplectic Geometry 53D40, 55N91 Given a symplectic manifold equipped with a Hamiltonian $G$-action and two $G$-invariant Lagrangians, we lift the construction of equivariant Lagrangian Floer homology of G.\@~Cazassus to the Novikov ring by constructing a ``quantum'' model in the vein of Biran and Cornea and Schmäschke. Using this refinement, we prove Cazassus' conjecture that, if the action on the zero-level of the moment map is free, then equivariant Floer homology agrees with the Floer homology of the Marsden-Weinstein reduction. |
| title | Equivariant Floer homology is isomorphic to reduced Floer homology |
| topic | Symplectic Geometry 53D40, 55N91 |
| url | https://arxiv.org/abs/2505.02647 |