Commuting tuples in reductive groups and their maximal compact subgroups

Pettet, Alexandra; Souto, Juan

doi:10.2140/gt.2013.17.2513

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Commuting tuples in reductive groups and their maximal compact subgroups

Alexandra Pettet and Juan Souto

Geometry & Topology 17 (2013) 2513–2593

DOI: 10.2140/gt.2013.17.2513

Abstract

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

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

Volume 17, issue 5 (2013)