Snowflake geometry in CAT(0) groups

TL;DR

This paper constructs CAT(0) groups with subgroups exhibiting a wide range of Dehn function behaviors, specifically for a dense set of exponents, expanding understanding of subgroup geometry in CAT(0) groups.

Contribution

It introduces new CAT(0) groups with subgroups having Dehn functions of the form x^s for a dense set of s in [2, ∞), revealing diverse geometric behaviors.

Findings

Existence of CAT(0) groups with subgroups having x^s Dehn functions for dense s

Expansion of known geometric behaviors of subgroups in CAT(0) groups

Demonstration of complex subgroup geometry within CAT(0) groups

Abstract

We construct CAT(0) groups containing subgroups whose Dehn functions are given by $x^s$, for a dense set of numbers $s \in [2, \infty)$. This significantly expands the known geometric behavior of subgroups of CAT(0) groups.