On the fundamental group of Hom(Z^k,G)
Algebraic Topology
2010-06-16 v1 Group Theory
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 \pi_1(G)^k.
Keywords
Cite
@article{arxiv.1006.3055,
title = {On the fundamental group of Hom(Z^k,G)},
author = {Jose Manuel Gomez and Alexandra Pettet and Juan Souto},
journal= {arXiv preprint arXiv:1006.3055},
year = {2010}
}