Hyperbolicity in non-metric cubical small-cancellation

Macarena Arenas, Kasia Jankiewicz, Daniel T. Wise

Published 2023-09-28Version 1

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.