Vol. 316, No. 1, 2022

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Divergence of finitely presented subgroups of CAT(0) groups

Noel Brady and Hung Cong Tran

Vol. 316 (2022), No. 1, 1–52
Abstract

We construct families of CAT (0) groups containing finitely presented groups whose divergence functions are of the form rα for a dense set of exponents α [2,) and rq log (r) for integers q 2. The same construction also yields examples of CAT (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
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