Equivariant Floer homology is isomorphic to reduced Floer homology

2025/05/05 by Julio Sampietro Christ, Christ, Julio Sampietro · 1 citation
Mathematics · Medicine · #53D40 #55N91 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2505.02647

openalex publication_date 2025/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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