Character varieties of virtually nilpotent Kähler groups and G-Higgs bundles

Abstract

Let G be a connected complex reductive affine algebraic group, and let K be a maximal compact subgroup. Let X be a compact connected Kähler manifold whose fundamental group Gamma is virtually nilpotent. We prove that the character variety Hom(Gamma, G)/G admits a natural strong deformation retraction to the subset Hom(Gamma, K)/K. The natural action of C^* on the moduli space of G-Higgs bundles over X extends to an action of C. This produces the deformation retraction.

References in corpus (4)

• The topology of moduli spaces of free group representations
• The topology of nilpotent representations in reductive groups and their maximal compact subgroups
• Higgs bundles over elliptic curves for complex reductive Lie groups
• Commuting elements in reductive groups and Higgs bundles on abelian varieties

Cited by in corpus (1)

• Flawed groups and the topology of character varieties