Uniform growth in small cancellation groups

16.04.2024 15:00 - 17:00

Markus Steenbock (Vienna)

We review known results and methods in the study of the uniform and uniform uniform growth rates of groups in settings of negative curvature. Then we pass on to the following result: the class of groups of uniform uniform exponential growth acting acylindrically on a hyperbolic space is closed under taking certain geometric small cancellation quotients. We explain two consequences: firstly, there is a finitely generated acylindrically hyperbolic group that has uniform exponential growth but has arbitrarily large torsion balls. Secondly, the uniform uniform exponential growth rate of every classical C''(l) small cancellation group, for sufficiently small l, is bounded from below by a universal positive constant. In particular, this constant does not depend on the hyperbolicity constant of the Cayley graph. Based on a joint work with X. Legaspi.


G. Arzhantseva, Ch. Cashen


SR 8, 2. OG, OMP 1