Hitchin components for orbifolds
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.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 arXiv:
 arXiv:1811.05366
 Bibcode:
 2018arXiv181105366A
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Algebraic Geometry;
 Mathematics  Differential Geometry
 EPrint:
 40 pages. v4: Same as v3, with minor corrections