Let G be a reductive algebraic group over C and let X be a smooth quasiprojective complex variety. Let us call a representation ρ : π1(X) → G to be G-rigid, if the set theoretic orbit of the representation ρ in the representation space Hom(π1(X), G) under the action of G is an open subset. Note that by fixing an embedding of G into a general linear group GLn(C), any representation ρ : π1(X) → G...