Residual $p$ properties of mapping class groups and surface groups
| dc.creator | Paris, Luis | |
| dc.date | 2007-03-23 | |
| dc.date.accessioned | 2026-07-07T07:53:25Z | |
| dc.date.available | 2026-07-07T07:53:25Z | |
| dc.description | Let $\mathcal M (Σ, \mathcal P)$ be the mapping class group of a punctured oriented surface $(Σ, \mathcal P)$ (where $\mathcal P$ may be empty), and let $\mathcal T_p(Σ,\mathcal P)$ be the kernel of the action of $\mathcal M (Σ, \mathcal P)$ on $H_1 (Σ\setminus \mathcal P, \mathbb F_p)$. We prove that $\mathcal T_p(Σ, \mathcal P)$ is residually $p$. In particular, this shows that $\mathcal M (Σ, \mathcal P)$ is virtually residually $p$. For a group $G$ we denote by $\mathcal I_p(G)$ the kernel of the natural action of ${\rm Out} (G)$ on $H_1(G, \mathbb F_p)$. In order to achieve our theorem, we prove that, under certain conditions ($G$ is conjugacy $p$-separable and has Property A), the group $\mathcal I_p(G)$ is residually $p$. The fact that free groups and surface groups have Property A is due to Grossman. The fact that free groups are conjugacy $p$-separable is due to Lyndon and Schupp. The fact that surface groups are conjugacy $p$-separable is, from a technical point of view, the main result of the paper. | |
| dc.identifier | https://arxiv.org/abs/math/0703703 | |
| dc.identifier | http://arxiv.org/abs/math/0703703 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126248 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F38 | |
| dc.title | Residual $p$ properties of mapping class groups and surface groups | |
| dc.type | text |