Divergence of finitely presented subgroups of CAT(0) groups

Noel Brady and Hung Cong Tran

Vol. 316 (2022), No. 1, 1–52

DOI: 10.2140/pjm.2022.316.1

Abstract

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

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