2007/03/23 by Luis Paris, Paris, Luis · 2 citations
Mathematics · #20F38 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:20F38
paper · pdf · doi:10.48550/arxiv.math/0703703
arxiv created 2007/03/23 · openalex publication_date 2007/03/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Tp(Σ,\mathcal P) be the kernel of the action of \mathcal M (Σ, \mathcal P) on H1 (Σ∖ \mathcal P, \mathbb Fp). We prove that \mathcal Tp(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 Ip(G) the kernel of the natural action of \rm Out (G) on H1(G, \mathbb Fp). In order to achieve our theorem, we prove that, under certain conditions (G is conjugacy p-separable and has Property A), the group \mathcal Ip(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.