On the cohomology rings of Hamiltonian T-spaces

Susan Tolman; Jonathan Weitsman

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On the cohomology rings of Hamiltonian T-spaces

Susan Tolman·Jonathan Weitsman

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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 \cite{K} the induced map $i^*:H_T^*(M) \to H_T^*(F)$ in equivariant cohomology is an injection. We give a simple proof of a formula of Goresky-Kottwitz-MacPherson \cite{GKM} for the image of the map $i^*$.

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BibTeX RIS

Susan Tolman, Jonathan Weitsman. 1998-12-02. On the cohomology rings of Hamiltonian T-spaces. https://arxiv.org/abs/math/9812006

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