Topology of character varieties of Abelian groups
Algebraic Geometry
2014-06-11 v3 Geometric Topology
Representation Theory
Abstract
Let G be a complex reductive algebraic group (not necessarily connected), let K be a maximal compact subgroup, and let A be a finitely generated Abelian group. We prove that the conjugation orbit space Hom(A,K)/K is a strong deformation retract of the GIT quotient space Hom(A,G)//G. As a corollary, we determine necessary and sufficient conditions for the character variety Hom(A,G)//G to be irreducible when G is connected and semisimple. For a general connected reductive G, analogous conditions are found to be sufficient for irreducibility, when A is free abelian.
Keywords
Cite
@article{arxiv.1301.7616,
title = {Topology of character varieties of Abelian groups},
author = {C. Florentino and S. Lawton},
journal= {arXiv preprint arXiv:1301.7616},
year = {2014}
}
Comments
33 pages; version 3: few small changes, one error corrected, one or two additional references; to appear in Topology and its Applications