Cohomology of mapping class groups and the abelian moduli space
| dc.creator | Andersen, Jørgen Ellegaard | |
| dc.creator | Villemoes, Rasmus | |
| dc.date | 2009-03-24 | |
| dc.date.accessioned | 2026-07-07T12:56:04Z | |
| dc.date.available | 2026-07-07T12:56:04Z | |
| dc.description | We consider a surface $Σ$ of genus $g \geq 3$, 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 $C^\infty(M)$ are modules over $Γ$. In this paper, we prove that both the cohomology groups $H^1(Γ, L^2(M))$ and $H^1(Γ, C^\infty(M))$ vanish. | |
| dc.description | 18 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0903.4045 | |
| dc.identifier | http://arxiv.org/abs/0903.4045 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224461 | |
| dc.subject | Differential Geometry | |
| dc.title | Cohomology of mapping class groups and the abelian moduli space | |
| dc.type | text |