Classifying semi-free Hamiltonian S¹-manifolds

2005/02/16 by Eduardo González, Gonzalez, Eduardo · 1 citation
Mathematics · #53D05 #53D20 #57R17 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.math/0502364

openalex publication_date 2005/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we describe a method to establish when a symplectic manifold M with semi-free Hamiltonian S¹-action is unique up to isomorphism (equivariant symplectomorphism). This will rely on a study of the symplectic topology of the reduced spaces. We prove that if the reduced spaces satisfy a rigidity condition, then the manifold M is uniquely determined by fixed point data. In particular we can prove that there is a unique family up to isomorphism of 6-dimensional symplectic manifolds with semi-free S¹-action and isolated fixed points.

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• On the equivariant cohomological rigidity of semi-free Hamiltonian circle actions

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