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arXiv · 1006.3055

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

Jose Manuel Gomez·Alexandra Pettet·Juan Souto
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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.

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Jose Manuel Gomez, Alexandra Pettet, Juan Souto. 2010-06-15. On the fundamental group of Hom(Z^k,G). https://arxiv.org/abs/1006.3055

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