Convex cocompact actions of relatively hyperbolic groups

Islam, Mitul¹ ; Zimmer, Andrew²

¹ Department of Mathematics, University of Michigan, Ann Arbor, MI, United States, Mathematisches Institut, Heidelberg University, Heidelberg, Germany
² Department of Mathematics, Louisiana State University, Baton Rouge, LA, United States, Department of Mathematics, University of Wisconsin, Madison, Madison, WI, United States

Geometry & topology, Tome 27 (2023) no. 2, pp. 417-511.

Résumé

We consider discrete groups in ${\mathrm{PGL}}_d(ℝ)$ 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 $\mathrm{CAT}(0)$ spaces.

Détail

DOI : 10.2140/gt.2023.27.417

Classification : 20F67, 20H10, 22E40, 53A20, 57N16
Keywords: convex real projective manifolds, relatively hyperbolic groups

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