We show the triviality of representations of the mapping class group of a genus g surface in GL(n, C), Diff (S) and Homeo(T) when appropriate restrictions on the genus g and the size of n hold. For example, if S is a surface of finite type with genus g > 3 and φ: MCG(S) → GL(n, C) is a homomorphism, then φ is trivial provided n < 2g. We also show that if S is a closed surface with genus g > 7, then every homomorphism φ: MCG(S) -y Diff(S 2) is trivial and that if g > 3, then every homomorphism φ: MCG(S) → Homeo(T2) is trivial.
ASJC Scopus subject areas
- Applied Mathematics