Globally stable cylinders for hyperbolic CAT(0) cube complexes

TL;DR

This paper proves that hyperbolic groups acting on CAT(0) cube complexes possess globally stable cylinders, confirming a conjecture for a broad class of hyperbolic groups.

Contribution

It establishes that all hyperbolic cubulated groups admit globally stable cylinders, advancing understanding of their geometric structure.

Findings

Hyperbolic cubulated groups admit globally stable cylinders

Supports Rips and Sela's conjecture for this class of groups

Enhances understanding of hyperbolic group geometry

Abstract

Rips and Sela introduced the notion of globally stable cylinders and asked if all Gromov hyperbolic groups admit such. We prove that hyperbolic cubulated groups admit globally stable cylinders.