On the fundamental group of Hom(Z^k,G)

Abstract

Let G be a compact Lie group, and consider the variety Hom(Z^k,G) of representations of Z^k into G. We view this as a based space by designating the trivial representation to be its base point. We prove that the fundamental group of this space is naturally isomorphic to π_1(G)^k.

References in corpus (1)

• Fundamental Groups of Commuting Elements in Lie Groups

Cited by in corpus (7)

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• A survey on spaces of homomorphisms to Lie groups
• On spaces of commuting elements in Lie groups
• Differentiable stratified groupoids and a de Rham theorem for inertia spaces