Homotopy type of free group character varieties
arXiv:1412.4396
Abstract
Let G be a real reductive algebraic group with maximal compact subgroup K, and let F be a rank r free group. Here, we summarize the construction of a natural strong deformation retraction from the space of closed orbits in Hom(F,G)/G to the orbit space Hom(F,K)/K. In particular, these spaces have the same homotopy type.
This is a 4 page summary of our paper "Topology of Moduli Spaces of Free Group Representations in Real Reductive Groups" (arXiv:1403.3603), it was accepted to appear in the Proceedings of the 2014 meeting of the Portuguese Society of Mathematics