Superexponential Dehn functions inside CAT(0) groups

Abstract

We construct 4-dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are ${\exp }^{(n)}(x^m)$ for integers $n,m\ge 1$ and 6-dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are ${\exp }^{(n)}(x^{\alpha })$ for integers $n\ge 1$ and $\alpha$ dense in $[1,\infty )$. This significantly expands the known geometric behavior of subgroups of CAT(0) groups.

38 pages, 7 figures, 1 table. Version 2 incorporates the referee's comments. To appear in Israel Journal of Mathematics