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. 25 (2023), no. 4, pp. 1285–1347DOI 10.4171/JEMS/1210