The topology of nilpotent representations in reductive groups and their maximal compact subgroups

Abstract

Let G be a complex reductive linear algebraic group and let K be a maximal compact subgroup of G. Given a nilpotent group Γgenerated by r elements, we consider the representation spaces Hom(Γ,G) and Hom(Γ,K) with the natural topology induced from an embedding into G^r and K^r respectively. The goal of this paper is to prove that there is a strong deformation retraction of Hom(Γ,G) onto Hom(Γ,K). We also obtain a strong deformation retraction of the geometric invariant theory quotient Hom(Γ,G)//G onto Hom(Γ,K)/K.

25 pages, minor changes, accepted for publication in Geometry and Topology

References in corpus (2)

• The topology of moduli spaces of free group representations
• On the fundamental group of Hom(Z^k,G)

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• Deformations of convex real projective manifolds and orbifolds
• Flawed groups and the topology of character varieties
• Character varieties of virtually nilpotent Kähler groups and G-Higgs bundles
• Geometry of $\mathrm{SU}(3)$-character varieties of torus knots
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• Torsion in the space of commuting elements in a Lie group
• Mixed Hodge structures on character varieties of nilpotent groups
• On GIT quotients and real forms
• The topology of Baumslag-Solitar representations
• On the moduli spaces of commuting elements in the projective unitary groups