An Isoperimetric Function for Bestvina-Brady Groups

TL;DR

This paper establishes that the Dehn function of any finitely presented Bestvina-Brady group is bounded above by a quartic polynomial, providing a sharp universal upper bound for these groups.

Contribution

It proves a universal quartic upper bound for the Dehn functions of all finitely presented Bestvina-Brady groups, advancing understanding of their geometric properties.

Findings

Dehn function of Bestvina-Brady groups is bounded by n^4

Quartic bound is optimal and universal for these groups

Enhances understanding of their geometric and algebraic complexity

Abstract

Given a right-angled Artin group A, the associated Bestvina-Brady group is defined to be the kernel of the homomorphism A \to \mathbb{Z} that maps each generator in the standard presentation of A to a fixed generator of \mathbb{Z}. We prove that the Dehn function of an arbitrary finitely presented Bestvina-Brady group is bounded above by n^4. This is the best possible universal upper bound.