Homotopy groups of moduli spaces of representations
Algebraic Geometry
2012-09-11 v4 Differential Geometry
Abstract
We calculate certain homotopy groups of the moduli spaces for representations of a compact oriented surface in the Lie groups GL(n,C) and U(p,q). Our approach relies on the interpretation of these representations in terms of Higgs bundles and uses Bott--Morse theory on the corresponding moduli spaces.
Cite
@article{arxiv.math/0506444,
title = {Homotopy groups of moduli spaces of representations},
author = {Steven B. Bradlow and Oscar Garcia-Prada and Peter B. Gothen},
journal= {arXiv preprint arXiv:math/0506444},
year = {2012}
}
Comments
21 pages; v2: improved results for moduli of representations in GL(n,C), provided proof of Proposition 4.13 (4.12 of v1) correcting argument given in earlier paper, other minor corrections; v3: corrected Remark 4.6, other minor corrections; v4: corrected statements of Proposition 4.17 and Theorems 4.19 and 4.22 (former Theorems 4.18 and 4.20); to appear in Topology