Let (S, *) be a closed oriented surface with a marked point, let G be a fixed group, and let ρ : π1(S) −→ G be a representation such that the orbit of ρ under the action of the mapping class group Mod(S, *) is finite. We prove that the image of ρ is finite. A similar result holds if π1(S) is replaced by the free group Fn on n ≥ 2 generators, and where Mod(S, *) is replaced by Aut(Fn). We show that if G is a linear algebraic group and if the representation variety of π1(S) is replaced by the

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... acter variety, then there are infinite image representations which are fixed by the whole mapping class group.