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arXiv · 2505.02647

Equivariant Floer homology is isomorphic to reduced Floer homology

Julio Sampietro Christ
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Abstract

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.

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Julio Sampietro Christ. 2025-05-05. Equivariant Floer homology is isomorphic to reduced Floer homology. https://arxiv.org/abs/2505.02647

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