Abstract
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 language | English |
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Journal | Quantum Topology |
Volume | 3 |
Issue number | 3/4 |
Pages (from-to) | 359-376 |
ISSN | 1663-487X |
DOIs | |
Publication status | Published - 2012 |
Externally published | Yes |