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

2010/06/15 by José Manuel Gómez, Jose Manuel Gomez, Alexandra Pettet +4 · 1 citation
Mathematics · Medicine · #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #math.AT #math.GR

paper · pdf · doi:10.48550/arxiv.1006.3055

arxiv created 2010/06/15 · openalex publication_date 2010/06/15 · arxiv updated 2010/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 π₁(G)^k.

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• Topology of character varieties of Abelian groups

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