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

AuthorsBradlow, Steven B.; García Prada, Oscar; Gothen, Peter B.
Issue Date27-Nov-2006
AbstractHiggs 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.
DescriptionVersion nr. 2 of the paper (2005/12/07) contains added due credits to the work of Burger, Iozzi and Wienhard. [Present] Version nr. 3 includes corrected count of connected components for G=SU(p,q) (p \neq q), added due credits to the work of Xia and Markman-Xia and minor corrections and clarifications.
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