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Convex cocompact actions of relatively hyperbolic groups

Mitul Islam and Andrew Zimmer

Geometry & Topology 27 (2023) 417–511
Abstract

We consider discrete groups in PGL d() acting convex cocompactly 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 and Kassel and is analogous to a result of Hruska and Kleiner for CAT (0) spaces.

Keywords
convex real projective manifolds, relatively hyperbolic groups
Mathematical Subject Classification 2010
Primary: 20F67, 20H10, 22E40
Secondary: 53A20, 57N16
References
Publication
Received: 28 October 2019
Revised: 20 July 2021
Accepted: 2 October 2021
Published: 16 May 2023
Proposed: Anna Wienhard
Seconded: Mladen Bestvina, Martin R Bridson
Authors
Mitul Islam
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States
Mathematisches Institut
Heidelberg University
Heidelberg
Germany
Andrew Zimmer
Department of Mathematics
Louisiana State University
Baton Rouge, LA
United States
Department of Mathematics
University of Wisconsin, Madison
Madison, WI
United States

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