Hyperbolicity in non-metric cubical small-cancellation

TL;DR

This paper establishes conditions under which certain non-metric cubical small-cancellation groups are hyperbolic, extending classical results about small-cancellation groups to a broader cubical setting.

Contribution

It generalizes the hyperbolicity result from classical small-cancellation groups to non-metric cubical small-cancellation quotients.

Findings

Hyperbolicity of quotients under non-metric cubical small-cancellation conditions

Extension of classical small-cancellation hyperbolicity results

Conditions ensuring hyperbolicity in non-positively curved cube complexes

Abstract

Given a non-positively curved cube complex $X$, we prove that the quotient of $\pi_1X$ defined by a cubical presentation $\langle X\mid Y_1,\dots, Y_s\rangle$ satisfying sufficient non-metric cubical small-cancellation conditions is hyperbolic provided that $\pi_1X$ is hyperbolic. This generalises the fact that finitely presented classical $C(7)$ small-cancellation groups are hyperbolic.