30 citations · 56 across the 15 of their papers we have counts for
18 papers
Convex cocompact groups with three-dimensional limit sets
Sami Douba, Gye-Seon Lee, Ludovic Marquis +1
We provide a general construction of convex cocompact hyperbolic reflection groups with three-dimensional limit sets. More precisely, our construction takes as input an arbitrary s…
Zariski-Closures of Linear Reflection Groups
Jacques Audibert, Sami Douba, Gye-Seon Lee +1
We give necessary and sufficient conditions for a linear reflection group in the sense of Vinberg to be Zariski-dense in the ambient projective general linear group. As an applicat…
Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere
Sami Douba, Gye-Seon Lee, Ludovic Marquis +1
We exhibit two examples of convex cocompact subgroups of the isometry groups of real hyperbolic spaces with limit set a Pontryagin sphere: one generated by reflections of $\ma…
Cusped Borel Anosov representations with positivity
Tengren Zhang, Gye-Seon Lee
We show that if a cusped Borel Anosov representation from a lattice to contains a unipotent element with a single…
Discrete Coxeter groups
Gye-Seon Lee, Ludovic Marquis
Coxeter groups are a special class of groups generated by involutions. They play important roles in the various areas of mathematics. This survey particularly focuses on how one us…
Deformation spaces of Coxeter truncation polytopes
Suhyoung Choi, Gye-Seon Lee, Ludovic Marquis
A convex polytope in the real projective space with reflections in the facets of is a Coxeter polytope if the reflections generate a subgroup of the group of projective…
Anosov triangle reflection groups in SL(3,R)
Gye-Seon Lee, Jaejeong Lee, Florian Stecker
We identify all Anosov representations of compact hyperbolic triangle reflection groups into the higher rank Lie group . Specifically, we prove that such…
Convex cocompactness for Coxeter groups
Jeffrey Danciger, François Guéritaud, Fanny Kassel +2
We investigate representations of Coxeter groups into as geometric reflection groups which are convex cocompact in the projective space $\mathbb{P}(\mat…
A small closed convex projective 4-manifold via Dehn filling
Gye-Seon Lee, Ludovic Marquis, Stefano Riolo
In order to obtain a closed orientable convex projective four-manifold with small positive Euler characteristic, we build an explicit example of convex projective Dehn filling of a…
Hitchin components for orbifolds
Daniele Alessandrini, Gye-Seon Lee, Florent Schaffhauser
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 compo…
Anti-de Sitter strictly GHC-regular groups which are not lattices
Gye-Seon Lee, Ludovic Marquis
For , we exhibit examples of strictly GHC-regular groups which are not quasi-isometric to the hyperbolic space , nor to any symm…
Convex projective generalized Dehn filling
Suhyoung Choi, Gye-Seon Lee, Ludovic Marquis
For , we exhibit the first examples of complete finite volume hyperbolic -manifolds with cusps such that infinitely many -orbifolds obtained from b…
Pappus Theorem, Schwartz Representations and Anosov Representations
Thierry Barbot, Gye-Seon Lee, Viviane Pardini Valério
In the paper "Pappus's theorem and the modular group", R. Schwartz constructed a 2-dimensional family of faithful representations of the modular group $\mathrm{PSL}(2,\mathbb…
Deformations of convex real projective manifolds and orbifolds
Suhyoung Choi, Gye-Seon Lee, Ludovic Marquis
In this survey, we study representations of finitely generated groups into Lie groups, focusing on the deformation spaces of convex real projective structures on closed manifolds a…
Convex projective structures on non-hyperbolic three-manifolds
Samuel A. Ballas, Jeffrey Danciger, Gye-Seon Lee
Y. Benoist proved that if a closed three-manifold M admits an indecomposable convex real projective structure, then M is topologically the union along tori and Klein bottles of fin…
Collar lemma for Hitchin representations
Gye-Seon Lee, Tengren Zhang
In this article, we prove an analog of the classical collar lemma in the setting of Hitchin representations.
Projective deformations of weakly orderable hyperbolic Coxeter orbifolds
Suhyoung Choi, Gye-Seon Lee
A Coxeter -orbifold is an -dimensional orbifold based on a polytope with silvered boundary facets. Each pair of adjacent facets meet on a ridge of some order , whose neigh…
Projective Deformations of Hyperbolic Coxeter 3-Orbifolds
Suhyoung Choi, Craig D. Hodgson, Gye-Seon Lee
By using Klein's model for hyperbolic geometry, hyperbolic structures on orbifolds or manifolds provide examples of real projective structures. By Andreev's theorem, many 3-dimensi…