The topology of Baumslag-Solitar representations

Abstract

Let $\Gamma =⟨a,b|a{b}^p{a}^{-1}=b^q⟩$ be a Baumslag--Solitar group and $G$ be a complex reductive algebraic group with maximal compact subgroup $K<G$. We show that, when $p$ and $q$ are relatively prime with distinct absolute values, there is a strong deformation retraction retraction of $Hom(\Gamma ,G)$ onto $Hom(\Gamma ,K)$.

13 pages, no figures