The topology of nilpotent representations in reductive groups and their maximal compact subgroups
Group Theory
2015-06-03 v2 Algebraic Geometry
Algebraic Topology
Geometric Topology
Representation Theory
Abstract
Let G be a complex reductive linear algebraic group and let K be a maximal compact subgroup of G. Given a nilpotent group \Gamma generated by r elements, we consider the representation spaces Hom(\Gamma,G) and Hom(\Gamma,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(\Gamma,G) onto Hom(\Gamma,K). We also obtain a strong deformation retraction of the geometric invariant theory quotient Hom(\Gamma,G)//G onto Hom(\Gamma,K)/K.
Keywords
Cite
@article{arxiv.1310.5109,
title = {The topology of nilpotent representations in reductive groups and their maximal compact subgroups},
author = {Maxime Bergeron},
journal= {arXiv preprint arXiv:1310.5109},
year = {2015}
}
Comments
25 pages, minor changes, accepted for publication in Geometry and Topology