2022/12/12 by Nicholas Stiles Wilkins, Wilkins, Nicholas
Mathematics · #14N35 #53D40 #53D45 #55N91 #57R19 #57R58 #57R91 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2212.06044
openalex publication_date 2022/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We demonstrate a way to apply S1-localisation to moduli spaces of holomorphic curves. We first prove a reinterpretation of Atyiah-Bott S1-localisation, called \it localisation by pseudocycles (LbP), for a smooth semifree S1-action on a manifold. We demonstrate that, for certain moduli spaces of holomorphic curves parametrised by some stratum of the homotopy quotient of a manifold, we may ``lift" the LbP procedure from the parameter space to the moduli space. As an application we deduce relations between equivariant symplectic classes and Gromov-Witten invariants, thus proving a conjecture of Seidel.