A cofinite universal space for proper actions for mapping class groups
| dc.creator | Ji, Lizhen | |
| dc.creator | Wolpert, Scott A. | |
| dc.date | 2008-11-24 | |
| dc.date | 2009-01-05 | |
| dc.date.accessioned | 2026-07-07T12:23:38Z | |
| dc.date.available | 2026-07-07T12:23:38Z | |
| dc.description | We prove that the mapping class group $Γ_{g,n}$ for surfaces of negative Euler characteristic has a cofinite universal space $\E$ for proper actions (the resulting quotient is a finite $CW$-complex). The approach is to construct a truncated Teichmueller space $\T_{g,n}(ε)$ by introducing a lower bound for the length of shortest closed geodesics and showing that $\T_{g,n}(ε)$ is a $Γ_{g,n}$ equivariant deformation retract of the Teichmueller space $\T_{g, n}$. The existence of such a cofinite universal space is important in the study of the cohomology of the group $\gag$. As an application, we note that there are only finitely many conjugacy classes of finite subgroups of $Γ_{g,n}$. Another application is that the rational Novikov conjecture in K-theory holds for $Γ_{g,n}$. | |
| dc.identifier | https://arxiv.org/abs/0811.3871 | |
| dc.identifier | http://arxiv.org/abs/0811.3871 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214058 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 57M07 (Primary) 30F60, 20F34 (Secondary) | |
| dc.title | A cofinite universal space for proper actions for mapping class groups | |
| dc.type | text |