Cubulating random quotients of hyperbolic cubulated groups

Abstract

We show that low-density random quotients of cubulated hyperbolic groups are again cubulated (and hyperbolic). Ingredients of the proof include cubical small-cancellation theory, the exponential growth of conjugacy classes, and the statement that hyperplane stabilizers grow exponentially more slowly than the ambient cubical group.

43 pages, 13 figures. v3 features improved exposition and references. This version to appear in Transactions of the AMS

References in corpus (5)

• Random groups do not have Property (T) at densities below 1/4
• Marked length spectrum rigidity from rigidity on subsets
• Approximating hyperbolic lattices by cubulations
• Property (T) in random quotients of hyperbolic groups at densities above 1/3
• Rigidity phenomena and the statistical properties of group actions on $\text{CAT}(0)$ cube complexes