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

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

2010-06-15

arxiv.org/abs/1006.3055v1

Mathematics

Algebraic Topology

Scientific paper

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 \pi_1(G)^k.

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