Restrictions of representations of a surface group to a pair of free subgroups

Research Report MRR97-031

Restrictions of representations of a surface group to a pair of free subgroups

B.M.S. Martin

Abstract: Let $\Pi$ be the fundamental group of a compact orientable genus m surface, and let G be a connected reductive algebraic group over an algebraically closed field of characteristic zero. We consider representations of $\Pi$ and of a certain pair of free subgroups A and B, into G. Restriction of representations induces a morphism from C $(\Pi,G)$ , the variety of conjugacy classes of representations of $\Pi$ , to C $(A,G)\times$ C(B,G). We prove that if m is large enough then this morphism is dominant and almost all fibres are finite. We interpret this as a rigidity result.

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