The topology of Baumslag-Solitar representations

Lior Silberman, Maxime Bergeron

Abstract: Let Γ=⟨a,b|abpa−1=bq⟩ 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(Γ,G) onto Hom(Γ,K).