Residual p properties of mapping class groups and surface groups

Let M(Σ,P) be the mapping class group of a punctured oriented surface (Σ,P) (where P may be empty), and let Tp(Σ,P) be the kernel of the action of M(Σ,P) on H1(Σ \ P ,Fp). We prove that Tp(Σ,P) is residually p. In particular, this shows that M(Σ,P) is virtually residually p. For a group G we denote by Ip(G) the kernel of the natural action of Out(G) on H1(G,Fp). In order to achieve our theorem, we prove that, under certain conditions (G is conjugacy p-separable and has Property A), the group 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. AMS Subject Classification. Primary: 20F38. Secondary: 20E26, 20F14, 20F34, 57M99.