Density of monodromy actions on non-abelian cohomology

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In this paper we study the monodromy action on the first Betti and de Rham non-abelian cohomology arising from a family of smooth curves. We describe sufficient conditions for the existence of a Zariski dense monodromy orbit. In particular we show that for a Lefschetz pencil of sufficiently high degree the monodromy action is dense.