Geometry & Topology

Commuting tuples in reductive groups and their maximal compact subgroups

Alexandra Pettet and Juan Souto

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

representations of abelian groups in Lie groups homotopy equivalences


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.

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