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Cohomology of mapping class groups and the abelian moduli space

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  • Jørgen Ellegaard Andersen, Denmark
  • Rasmus Villemoes, Denmark
We consider a surface Σ of genus g≥3 , either closed or with exactly one puncture. The mapping class group Γ of Σ acts symplectically on the abelian moduli space M=Hom(π 1 (Σ),U(1))=Hom(H 1 (Σ),U(1)) , and hence both L 2 (M) and C ∞ (M) are modules over Γ . In this paper, we prove that both the cohomology groups H 1 (Γ,L 2 (M)) and H 1 (Γ,C ∞ (M)) vanish.
Original languageEnglish
JournalQuantum Topology
Pages (from-to)359-376
Publication statusPublished - 2012

    Research areas

  • mapping class groups, group cohomology, moduli spaces, property (T)

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