Divergence of finitely presented groups

Abstract

We construct families of finitely presented groups exhibiting new divergence behavior; we obtain divergence functions of the form $r^{\alpha }$ for a dense set of exponents $\alpha \in [2,\infty )$ and $r^n\log (r)$ for integers $n\ge 2$. The same construction also yields examples of finitely presented groups which contain Morse elements that are not contracting.

23 pages, 2 figures. Version 2 incorporates the referee's comments. To appear in Groups, Geometry, and Dynamics