On Dimensions of Representation Varieties of Baumslag-Solitar Groups

Abstract

This article concerns representations of a specific collection of finitely-presented groups, the Baumslag-Solitar groups. We prove that there exist arbitrary-dimensional simple representations for a specific sub-collection of Baumslag-Solitar groups. We then apply this fact, along with Fox Calculus, to compute the dimension of the tangent space to the representation scheme at these particular simple representations. A discussion of the deformations of these simple representations leads to the dimension of the representation variety and representation scheme.