Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces

Research paper by Steven B. Bradlow, Oscar Garcia-Prada, Peter B. Gothen

Indexed on: 27 Nov '06Published on: 27 Nov '06Published in: Mathematics - Algebraic Geometry


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.