Hitchin components for orbifolds
Geometric Topology
2020-10-28 v5 Algebraic Geometry
Differential Geometry
Abstract
We extend the notion of Hitchin component from surface groups to orbifold groups and prove that this gives new examples of higher Teichm\"{u}ller 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 -manifolds.
Keywords
Cite
@article{arxiv.1811.05366,
title = {Hitchin components for orbifolds},
author = {Daniele Alessandrini and Gye-Seon Lee and Florent Schaffhauser},
journal= {arXiv preprint arXiv:1811.05366},
year = {2020}
}
Comments
43 pages. v5: Final version, to appear in JEMS