An isoperimetric function for Bestvina-Brady groups

Abstract

Given a right-angled Artin group A, the associated Bestvina–Brady group is defined to be the kernel of the homomorphism A → ℤ that maps each generator in the standard presentation of A to a fixed generator of ℤ. We prove that the Dehn function of an arbitrary finitely presented Bestvina–Brady group is bounded above by n4. This is the best possible universal upper bound.