Commuting tuples in reductive groups and their maximal compact subgroups

Pettet, Alexandra¹ ; Souto, Juan²

¹ Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada
² Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada

Geometry & topology, Tome 17 (2013) no. 5, pp. 2513-2593.

Résumé

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

Détail

DOI : 10.2140/gt.2013.17.2513

Classification : 20G20, 55P99
Keywords: representations of abelian groups in Lie groups, homotopy equivalences

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