On Lipschitz functions on groups equipped with conjugation-invariant norms

2022/04/20 by Kędra, Jarek · 2 citations
#FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2204.09373

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.

Cited by

• Almost-invariant elements of group actions on Lip₀ spaces
• The infinite dimensional geometry of conjugation invariant generating sets

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