Divergence of finitely presented subgroups of CAT(0) groups

Abstract

We construct families of $CAT(0)$ 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 $r^q\log (r)$ for integers $q\ge 2$. The same construction also yields examples of $CAT(0)$ groups containing contracting elements which are not contracting in certain finitely presented subgroups.

39 pages, 6 figures, and 1 table. The proof of the main divergence theorem in this paper is similar in outline to that in arXiv:2002.03653 but there are significant technical differences

References in corpus (2)

• On metric relative hyperbolicity
• A remark on thickness of free-by-cyclic groups

Cited by in corpus (2)

• Morse elements in Garside groups are strongly contracting
• Divergence, thickness and hypergraph index for general Coxeter groups