English

Convex co-compact actions of relatively hyperbolic groups

Geometric Topology 2023-05-24 v2 Differential Geometry

Abstract

In this paper we consider discrete groups in PGLd(R){\rm 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-Gu\'eritaud-Kassel and is analogous to a result of Hruska-Kleiner for CAT(0){\rm CAT}(0) spaces.

Keywords

Cite

@article{arxiv.1910.08885,
  title  = {Convex co-compact actions of relatively hyperbolic groups},
  author = {Mitul Islam and Andrew Zimmer},
  journal= {arXiv preprint arXiv:1910.08885},
  year   = {2023}
}

Comments

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

R2 v1 2026-06-23T11:48:47.693Z