Communications in Analysis and Geometry

Volume 11 (2003)

Number 4

The Cohomology Rings of Symplectic Quotients

Pages: 751 – 773

DOI: http://dx.doi.org/10.4310/CAG.2003.v11.n4.a6

Authors

Susan Tolman

Jonathan Weitsman

Abstract

Let (M, ω) be a symplectic manifold, equipped with a Hamiltonian action of a compact Lie group G. We give an explicit formula for the cohomology ring of the symplectic quotient M//G in terms of the cohomology ring of M and fixed point data. Under certain conditions, our formula also holds for the integral cohomology ring, and can be used to show that the cohomology of the reduced space is torsion-free.

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