On cubulated relatively hyperbolic groups

Reyes, Eduardo

doi:10.2140/gt.2023.27.575

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On cubulated relatively hyperbolic groups

Eduardo Reyes

Geometry & Topology 27 (2023) 575–640

DOI: 10.2140/gt.2023.27.575

Abstract

We show that properly and cocompactly cubulated relatively hyperbolic groups are virtually special, provided the peripheral subgroups are virtually special in a way that is compatible with the cubulation. This extends Agol’s result for cubulated hyperbolic groups, and applies to a wide range of peripheral subgroups. In particular, we deduce virtual specialness for properly and cocompactly cubulated groups that are hyperbolic relative to virtually abelian groups. As another consequence, by using a theorem of Martin and Steenbock we obtain virtual specialness for groups obtained as a quotient of a free product of finitely many virtually compact special groups by a finite set of relators satisfying the classical $C^{'} (\frac{1}{6})$ –small cancellation condition.

Keywords

CAT(0) cube complexes, relatively hyperbolic groups, virtual specialness

Mathematical Subject Classification

Primary: 20F65

Secondary: 20F67, 57M07

References

Publication

Received: 2 June 2020

Revised: 1 March 2021

Accepted: 16 November 2021

Published: 16 May 2023

Proposed: Martin R Bridson

Seconded: Mladen Bestvina, David Fisher

Authors

Eduardo Reyes
Department of Mathematics University of California at Berkeley Berkeley, CA United States

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Volume 27, issue 2 (2023)