Conjugator length of Bestvina-Brady groups

Abstract

We classify the conjugator length functions of Bestvina-Brady groups. We show that the conjugator length function, when non-trivial, grows as a linear or quadratic polynomial. In fact, we give explicit criteria on the defining graph to determine the precise degree of the polynomial. The proof generalises ideas of Bridson, Riley, and Sale by exploiting the framework developed by Chang and the authors to classify the Dehn functions of Bestvina-Brady groups.