#### Volume 17, issue 5 (2013)

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Commuting tuples in reductive groups and their maximal compact subgroups

### Alexandra Pettet and Juan Souto

Geometry & Topology 17 (2013) 2513–2593
##### Abstract

Let $G$ be a reductive algebraic group and $K\subset G$ a maximal compact subgroup. We consider the representation spaces $Hom\left({ℤ}^{k},K\right)$ and $Hom\left({ℤ}^{k},G\right)$ with the topology induced from an embedding into ${K}^{k}$ and ${G}^{k}$, respectively. The goal of this paper is to prove that $Hom\left({ℤ}^{k},K\right)$ is a strong deformation retract of $Hom\left({ℤ}^{k},G\right)$.

##### Keywords
representations of abelian groups in Lie groups, homotopy equivalences
Primary: 20G20
Secondary: 55P99