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Geometriae Dedicata

, 122:185 | Cite as

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

  • Steven B. Bradlow
  • Oscar García-Prada
  • Peter B. Gothen
Original Paper

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

Keywords

Hermitian symmetric spaces Higgs bundles 

Mathematics Subject Classification

Primary 14H60 Secondary 57R57 Secondary 58D29 

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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  • Steven B. Bradlow
    • 1
  • Oscar García-Prada
    • 2
  • Peter B. Gothen
    • 3
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA
  2. 2.Departamento de MatemáticasCSICMadridSpain
  3. 3.Departamento de Matemática Pura, Faculdade de CiênciasUniversidade do PortoPortoPortugal

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