Higgs bundles for the non-compact dual of the special orthogonal group

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

Research output: Contribution to journalArticlepeer-review

Abstract

Higgs bundles over a closed orientable surface can be defined for any real reductive Lie group $$G$$G. In this paper we examine the case G=SO∗(2n). We describe a rigidity phenomenon encountered in the case of maximal Toledo invariant. Using this and Morse theory in the moduli space of Higgs bundles, we show that the moduli space is connected in this maximal Toledo case. The Morse theory also allows us to show connectedness when the Toledo invariant is zero. The correspondence between Higgs bundles and surface group representations thus allows us to count the connected components with zero and maximal Toledo invariant in the moduli space of representations of the fundamental group of the surface in SO∗(2n).

Original languageEnglish (US)
Pages (from-to)1-48
Number of pages48
JournalGeometriae Dedicata
Volume175
Issue number1
DOIs
StatePublished - Apr 1 2015

Keywords

  • Higgs bundles
  • Moduli spaces
  • Real Lie groups
  • Surface group representations

ASJC Scopus subject areas

  • Geometry and Topology

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