JournalsjemsOnline First14 February 2022

Hitchin components for orbifolds

  • Daniele Alessandrini

    Columbia University, New York, USA
  • Gye-Seon Lee

    Sungkyunkwan University, Suwon, South Korea
  • Florent Schaffhauser

    Université de Strasbourg, France; Universidad de Los Andes, Bogotá, Colombia
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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.

Cite this article

Daniele Alessandrini, Gye-Seon Lee, Florent Schaffhauser, Hitchin components for orbifolds. J. Eur. Math. Soc. (2022), published online first

DOI 10.4171/JEMS/1210