Local coordinates for \operatorname{SL}(n,\mathbf{C})-character varieties of finite-volume hyperbolic 3-manifolds
Local coordinates for \operatorname{SL}(n,\mathbf{C})-character varieties of finite-volume hyperbolic 3-manifolds
Given a finite-volume hyperbolic 3-manifold, we compose a lift of the holonomy in SL(2,C) with the n-dimensional irreducible representation of SL(2,C) in SL(n,C). In this paper we give local coordinates of the SL(n,C)-character variety around the character of this representation. As a corollary, this representation is isolated among all representations …