Divergence of finitely presented subgroups of CAT(0) groups

We construct families of $CAT (0)$ groups containing finitely presented groups whose divergence functions are of the form $r^{α}$ for a dense set of exponents $α \in [2, \infty)$ and $r^{q} \log (r)$ for integers $q \geq 2$ . The same construction also yields examples of $CAT (0)$ groups containing contracting elements which are not contracting in certain finitely presented subgroups.

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Keywords

group divergence, CAT(0) groups, contracting elements

Mathematical Subject Classification

Primary: 20F65, 20F67

Milestones

Received: 9 March 2021

Revised: 2 September 2021

Accepted: 13 November 2021

Published: 26 February 2022

Authors

Noel Brady
Department of Mathematics The University of Oklahoma Norman, OK United States

Hung Cong Tran
Department of Mathematics The University of Oklahoma Norman, OK United States

Vol. 316, No. 1, 2022

Noel Brady and Hung Cong Tran

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors