Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces
Algebraic Geometry
2012-09-11 v3 Differential Geometry
Abstract
Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo invariant.
Cite
@article{arxiv.math/0511415,
title = {Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces},
author = {Steven B. Bradlow and Oscar Garcia-Prada and Peter B. Gothen},
journal= {arXiv preprint arXiv:math/0511415},
year = {2012}
}
Comments
v2: added due credits to the work of Burger, Iozzi and Wienhard. v3: corrected count of connected components for G=SU(p,q) (p \neq q); added due credits to the work of Xia and Markman-Xia; minor corrections and clarifications. 31 pages