Singularities of free group character varieties
Algebraic Geometry
2012-11-19 v4 Geometric Topology
Representation Theory
Abstract
Let X be the moduli space of SL(n,C), SU(n), GL(n,C), or U(n)-valued representations of a rank r free group. We classify the algebraic singular stratification of X. This comes down to showing that the singular locus corresponds exactly to reducible representations if there exist singularities at all. Then by relating algebraic singularities to topological singularities, we show the moduli spaces X generally are not topological manifolds, except for a few examples we explicitly describe.
Keywords
Cite
@article{arxiv.0907.4720,
title = {Singularities of free group character varieties},
author = {Carlos Florentino and Sean Lawton},
journal= {arXiv preprint arXiv:0907.4720},
year = {2012}
}
Comments
33 pages. Version 4 is shorter and more focused; cut material will be expanded upon and written up in subsequent papers. Clarifications, and expository revisions have been added. Accepted for publication in Pacific Journal of Mathematics