Representations of Surface Groups with Finite Mapping Class Group Orbits

Abstract

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… (More)

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