Representations of knot groups into SL<inf>n</inf>(C) and twisted Alexander polynomials

©2015 Mathematical Sciences Publishers. Let Γ be the fundamental group of the exterior of a knot in the three-sphere. We study deformations of representations of 0 into SLn(C) which are the sum of two irreducible representations. For such representations we give a necessary condition, in terms of the twisted Alexander polynomial, for the existence of irreducible deformations. We also give a more restrictive sufficient condition for the existence of irreducible deformations. We also prove a duality theorem for twisted Alexander polynomials and we describe the local structure of the representation and character varieties.