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On Lipschitz functions on groups equipped with conjugation-invariant norms (2204.09373v3)
Published 20 Apr 2022 in math.GR and math.MG
Abstract: We observe that a function on a group equipped with a bi-invariant word metric is Lipschitz if and only if it is a partial quasimorphism bounded on the generating set. We also show that an undistorted element is always detected by an antisymmetric homogeneous partial quasimorphisms. We provide a general homogenisation procedure for Lipschitz functions and relate partial quasimorphisms on a group to ones on its asymptotic cones.
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