The topology of moduli spaces of free group representations
General Topology
2009-07-28 v2 Algebraic Geometry
Geometric Topology
Abstract
For any complex affine reductive group G and a fixed choice of maximal compact subgroup K, we show that the G-character variety of a free group strongly deformation retracts to the corresponding K-character space, which is a real semi-algebraic set. Combining this with constructive invariant theory and classical topological methods, we show that the SL(3,C)-character variety of a rank 2 free group is homotopic to an 8 sphere and the SL(2,C)-character variety of a rank 3 free group is homotopic to a 6 sphere.
Keywords
Cite
@article{arxiv.0807.3317,
title = {The topology of moduli spaces of free group representations},
author = {Carlos Florentino and Sean Lawton},
journal= {arXiv preprint arXiv:0807.3317},
year = {2009}
}
Comments
37 pages, 2 figures, version 2 corrects typos, generalizes context, and adds a corollary, it is the accepted version to appear in Mathematische Annalen