Convex projective generalized Dehn filling

Suhyoung Choi (1) , Gye-Seon Lee (2) , Ludovic Marquis (3)

1 KAIST - Korea Advanced Institute of Science and Technology
2 Universität Heidelberg [Heidelberg] = Heidelberg University
3 IRMAR - Institut de Recherche Mathématique de Rennes

In dimension $d = 4, 5, 6, 7$, we find the first examples of complete finite volume hyperbolic $d$-dimensional manifolds $M$ with cusps such that an infinite number of orbifolds $M_m$ obtained by generalized Dehn fillings on $M$ admit a properly convex real projective structure. The manifolds $M$ are covering of hyperbolic Coxeter orbifolds and the orbifold fundamental groups $\Gamma_m$ of $M_m$ are Gromov hyperbolic relative to a collection of subgroups virtually isomorphic to $\mathbb{Z}^{d−2}.

Mots clés: Hilbert Geometry; Coxeter group; Dehn Filling; Real projective structure; Orbifold

Domaines: Topologie géométrique [math.GT]

Suhyoung Choi, Gye-Seon Lee, Ludovic Marquis. Convex projective generalized Dehn filling. Annales Scientifiques de l'École Normale Supérieure, 2020, 53 (1), pp.217-266. ⟨10.24033/asens.2421⟩. ⟨hal-01393971v2⟩