## Geometry & Topology

### Commuting tuples in reductive groups and their maximal compact subgroups

#### Abstract

Let $G$ be a reductive algebraic group and $K⊂G$ a maximal compact subgroup. We consider the representation spaces $Hom(ℤk,K)$ and $Hom(ℤk,G)$ with the topology induced from an embedding into $Kk$ and $Gk$, respectively. The goal of this paper is to prove that $Hom(ℤk,K)$ is a strong deformation retract of $Hom(ℤk,G)$.

#### Article information

Source
Geom. Topol., Volume 17, Number 5 (2013), 2513-2593.

Dates
Accepted: 5 May 2013
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732683

Digital Object Identifier
doi:10.2140/gt.2013.17.2513

Mathematical Reviews number (MathSciNet)
MR3190294

Zentralblatt MATH identifier
1306.55007

#### Citation

Pettet, Alexandra; Souto, Juan. Commuting tuples in reductive groups and their maximal compact subgroups. Geom. Topol. 17 (2013), no. 5, 2513--2593. doi:10.2140/gt.2013.17.2513. https://projecteuclid.org/euclid.gt/1513732683

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