The cohomology rings of symplectic quotients

Susan Tolman, Jonathan Weitsman

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)751-773
Number of pages23
JournalCommunications in Analysis and Geometry
Issue number4
StatePublished - Sep 2003

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty


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