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

Steven B. Bradlow·Oscar Garcia-Prada·Peter B. Gothen
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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.

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Steven B. Bradlow, Oscar Garcia-Prada, Peter B. Gothen. 2005-11-16. Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces. https://doi.org/10.1007/s10711-007-9127-y

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