An Isoperimetric Function for Bestvina-Brady Groups

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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.