Cohomology of mapping class groups and the abelian moduli space
نویسندگان
چکیده
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(π1(Σ), U(1)) = Hom(H1(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 H1(Γ, L2(M)) and H1(Γ,C∞(M)) vanish.
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