The Dehn functions of Stallings-Bieri groups

TL;DR

This paper proves that Stallings-Bieri groups and some related Bestvina-Brady groups have quadratic Dehn functions, indicating their geometric complexity grows quadratically with word length.

Contribution

It establishes the quadratic Dehn function property for Stallings-Bieri and certain Bestvina-Brady groups, expanding understanding of their geometric group theory characteristics.

Findings

Stallings-Bieri groups have quadratic Dehn functions.

Certain Bestvina-Brady groups also exhibit quadratic Dehn functions.

Results contribute to the classification of groups by their Dehn functions.

Abstract

We show that the Stallings-Bieri groups, along with certain other Bestvina-Brady groups, have quadratic Dehn function.