# Members & Guests

## Dr. Gye Seon Lee

Ruprecht-Karls-Universität Heidelberg

E-mail: lee(at)mathi.uni-heidelberg.de
Telephone: +49-6221-54-14219
Homepage: https://www.mathi.uni-heidelberg.de/~lee...

## Project

1Hitchin components for orbifolds

## Publications within SPP2026

For d = 4, 5, 6, 7, 8, we exhibit examples of $$\mathrm{AdS}^{d,1}$$ strictly GHC-regular groups which are not quasi-isometric to the hyperbolic space $$\mathbb{H}^d$$, nor to any symmetric space. This provides a negative answer to Question 5.2 in a work of Barbot et al. and disproves Conjecture 8.11 of Barbot-Mérigot [Groups Geom. Dyn. 6 (2012), pp. 441-483].

We construct those examples using the Tits representation of well-chosen Coxeter groups. On the way, we give an alternative proof of Moussong's hyperbolicity criterion (Ph.D. Thesis) for Coxeter groups built on Danciger-Guéritaud-Kassel's 2017 work and find examples of Coxeter groups W such that the space of strictly GHC-regular representations of W into $$\mathrm{PO}_{d,2}(\mathbb{R})$$ up to conjugation is disconnected.

 Journal Transactions of the American Mathematical Society Volume 372 Pages 153-186 Link to preprint version Link to published version

Related project(s):
1Hitchin 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 Teichmüller spaces. We show that the Hitchin component of an orbifold group is homeomorphic to an open ball, and we compute its dimension explicitly. For example, the Hitchin component of the right-angled hyperbolic $$\ell$$-polygon reflection group into $$\mathrm{PGL}(2m,\mathbb{R})$$, resp. $$\mathrm{PGL}(2m+1,\mathbb{R})$$, is homeomorphic to an open ball of dimension $$(\ell-4)m^2+1$$, resp. $$(\ell-4)(m^2+m)$$. We also give applications to the study of the pressure metric and the deformation theory of real projective structures on 3-manifolds.