On cubulated relatively hyperbolic groups

Reyes, Eduardo¹

¹ Department of Mathematics, University of California at Berkeley, Berkeley, CA, United States

Geometry & topology, Tome 27 (2023) no. 2, pp. 575-640.

Résumé

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 $C^{\prime }\left(\frac{1}{6}\right)$–small cancellation condition.

Détail

DOI : 10.2140/gt.2023.27.575

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

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