Mathematische Zeitschrift

, Volume 271, Issue 1–2, pp 33–44 | Cite as

On the fundamental group of \({{\rm Hom}({\mathbb Z}^k,G)}\)

  • José Manuel Gómez
  • Alexandra Pettet
  • Juan Souto
Article

Abstract

Let G be a compact Lie group. Consider the variety \({{\rm Hom}({\mathbb Z}^{k},G)}\) of representations of \({{\mathbb Z}^k}\) into G. We can see this as a based space by taking as base point the trivial representation
. The goal of this paper is to prove that \({\pi_1({\rm Hom}({\mathbb Z}^k,G))}\) is naturally isomorphic to π1(G)k.

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • José Manuel Gómez
    • 1
  • Alexandra Pettet
    • 2
    • 3
  • Juan Souto
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA
  3. 3.Mathematical InstituteUniversity of OxfordOxfordUK

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