On the cohomology rings of Hamiltonian T-spaces

1998/12/01 by Susan Tolman, Tolman, Susan, Jonathan Weitsman +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AG #math.AT #math.DG #math.SG

paper · pdf · doi:10.48550/arxiv.math/9812006

correction to references

openalex publication_date 1998/12/01 · arxiv created 1998/12/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a symplectic manifold equipped with a Hamiltonian action of a torus T. Let F denote the fixed point set of the T-action and let i:F\hookrightarrow M denote the inclusion. By a theorem of F. Kirwan \citeK the induced map i^*:H_T^*(M) → H_T^*(F) in equivariant cohomology is an injection. We give a simple proof of a formula of Goresky-Kottwitz-MacPherson \citeGKM for the image of the map i^*.

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