Commuting elements in reductive groups and Higgs bundles on abelian varieties

Abstract

Let G be a connected real reductive algebraic group, and let K be a maximal compact subgroup of G. We prove that the conjugation orbit space Hom(Z^{2d},K)/K is a strong deformation retract of the space Hom(Z^{2d},G)/G of equivalence classes of representations of Z^{2d} into G. This is proved by showing that the homotopy type of the moduli space of principal G-Higgs bundles of vanishing rational characteristic classes on a complex abelian variety of dimension d depends only on K.

References in corpus (1)

• Yang-Mills equation for stable Higgs sheaves

Cited by in corpus (3)

• Hodge-Deligne polynomials of character varieties of abelian groups
• Character varieties of virtually nilpotent Kähler groups and G-Higgs bundles
• Yang-Mills-Higgs connections on Calabi-Yau manifolds, II