Geometry & Topology

Commuting tuples in reductive groups and their maximal compact subgroups

Alexandra Pettet and Juan Souto

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Abstract

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

Article information

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

Dates
Received: 7 June 2012
Accepted: 5 May 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 20G20: Linear algebraic groups over the reals, the complexes, the quaternions
Secondary: 55P99: None of the above, but in this section

Keywords
representations of abelian groups in Lie groups homotopy equivalences

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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