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

Steven B. Bradlow, Oscar García-Prada, Peter B. Gothen

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)185-213
Number of pages29
JournalGeometriae Dedicata
Volume122
Issue number1
DOIs
StatePublished - Oct 2006

Keywords

  • Hermitian symmetric spaces
  • Higgs bundles

ASJC Scopus subject areas

  • Geometry and Topology

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