The action of the Torelli group on the homology of representation spaces is nontrivial *

S. E. Cappell, R. Lee, E. Y. Miller

Research output: Contribution to journalArticle

Abstract

The mapping class group and its subgroup, the Torelli group, of a Riemann surface M has a natural action on the space RSU(2)(M) of SU(2)-representations of the fundamental group of M and its subspace RSU(2)(M))irred of irreducibles. In this paper we compute the cohomology H* (RSU(2)(M)), H* (RSU(2)M(M)irred) of both of these spaces and show that the induced action of the Torelli group is non-trivial.

Original languageEnglish (US)
Pages (from-to)851-871
Number of pages21
JournalTopology
Volume39
Issue number4
DOIs
StatePublished - Jul 2000

Keywords

  • Gauge theory
  • Mapping class group
  • Moduli space
  • Representation variety
  • Torelli group

ASJC Scopus subject areas

  • Geometry and Topology

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