Convex co-compact actions of relatively hyperbolic groups

Abstract

In this paper we consider discrete groups in ${\mathrm{PGL}}_d(\mathbb{R})$ acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establish necessary and sufficient conditions for the group to be relatively hyperbolic in terms of the geometry of the convex domain. This answers a question of Danciger-Guéritaud-Kassel and is analogous to a result of Hruska-Kleiner for $\mathrm{CAT}(0)$ spaces.

Minor revisions, final version to appear in Geometry & Topology. 96 pages, 2 figures. Comments welcome

References in corpus (4)

• A flat torus theorem for convex co-compact actions of projective linear groups
• Relatively dominated representations
• Codimension-$1$ Simplices in Divisible Convex Domains
• Groupes convexes-cocompacts en rang supérieur

Cited by in corpus (5)

• Rank One Hilbert Geometries
• Patterson--Sullivan densities in convex projective geometry
• Convex co-compact representations of 3-manifold groups
• The structure of relatively hyperbolic groups in convex real projective geometry
• Convex co-compact groups with one dimensional boundary faces