Volume 17, issue 5 (2013)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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 G 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).

Keywords
representations of abelian groups in Lie groups, homotopy equivalences
Mathematical Subject Classification 2010
Primary: 20G20
Secondary: 55P99
References
Publication
Received: 7 June 2012
Accepted: 5 May 2013
Published: 18 September 2013
Proposed: Benson Farb
Seconded: Jesper Grodal, Leonid Polterovich
Authors
Alexandra Pettet
Department of Mathematics
University of British Columbia
1984 Mathematics Road
Vancouver, BC V6T 1Z2
Canada
Juan Souto
Mathematics Department
University of British Columbia
1984 Mathematics Road
Vancouver, BC V6T 1Z2
Canada
http://www.math.ubc.ca/~jsouto