Groups with quadratic-non-quadratic Dehn functions

TL;DR

This paper constructs a finitely presented group with a Dehn function that is not quadratic overall but can be bounded by a quadratic function over long intervals, challenging previous assumptions about Dehn function behavior.

Contribution

It introduces a new example of a finitely presented group with a Dehn function exhibiting non-quadratic growth, yet locally bounded by quadratic functions.

Findings

Existence of a finitely presented group with non-quadratic Dehn function.

Dehn function can be majorized by quadratic functions on long intervals.

Challenges previous beliefs about the growth behavior of Dehn functions.

Abstract

We construct a finitely presented group $G$ with non-quadratic Dehn function $f$ majorizable by a quadratic function on arbitrary long intervals.