Hitchin components for orbifolds

Daniele Alessandrini, Gye Seon Lee, Florent Schaffhauser

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We extend the notion of Hitchin component from surface groups to orbifold groups and prove that this gives new examples of higher Teichmüller spaces. We show that the Hitchin component of an orbifold group is homeomorphic to an open ball and we compute its dimension explicitly. We then give applications to the study of the pressure metric, cyclic Higgs bundles, and the deformation theory of real projective structures on 3-manifolds.

Original languageEnglish
Pages (from-to)1285-1347
Number of pages63
JournalJournal of the European Mathematical Society
Volume25
Issue number4
DOIs
StatePublished - 2023

Keywords

  • Coxeter group
  • Hitchin component
  • Teichmüller space
  • orbifold
  • real projective structure

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