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arXiv · 2204.09373

On Lipschitz functions on groups equipped with conjugation-invariant norms

Jarek Kędra
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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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Jarek Kędra. 2022-04-20. On Lipschitz functions on groups equipped with conjugation-invariant norms. https://arxiv.org/abs/2204.09373

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