Super-exponential 2-dimensional Dehn functions

TL;DR

This paper constructs groups with 2-dimensional Dehn functions that grow as towers of exponentials, demonstrating complex geometric properties in group theory.

Contribution

It introduces new examples of groups with super-exponential 2-dimensional Dehn functions of arbitrary height, expanding understanding of geometric group theory.

Findings

Groups with 2-dimensional Dehn functions of the form exp^n(x) for any natural n

Demonstrates the existence of groups with highly complex isoperimetric functions

Advances the classification of Dehn functions in geometric group theory

Abstract

We produce examples of groups of type F_3 with 2-dimensional Dehn functions of the form exp^n(x) (a tower of exponentials of height n), where n is any natural number.