Hitchin components for orbifolds

We extend the notion of Hitchin component from surface groups to orbifold groups and prove that this gives new examples of higher Teichmuller 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.

Automated summary

We extend the notion of Hitchin component to orbifold groups and explore its properties. Specifically, we prove that the Hitchin component of an orbifold group is homeomorphic to an open ball and compute its dimension explicitly. Furthermore, we demonstrate its applications to pressure metric, cyclic Higgs bundles, and deformation theory of real projective structures on 3-manifolds.