Character varieties of virtually nilpotent K\"ahler groups and G-Higgs bundles
Algebraic Geometry
2021-05-25 v2
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 K\"ahler 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.
Keywords
Cite
@article{arxiv.1405.0610,
title = {Character varieties of virtually nilpotent K\"ahler groups and G-Higgs bundles},
author = {Indranil Biswas and Carlos Florentino},
journal= {arXiv preprint arXiv:1405.0610},
year = {2021}
}