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The topology of Baumslag-Solitar representations (1902.04046v1)
Published 11 Feb 2019 in math.AT, math.GR, math.GT, and math.RT
Abstract: Let $\Gamma=\langle a,b | a b{p} a{-1} = b{q}\rangle$ 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 $Hom(\Gamma,K)$.