Directional asymptotic cones of groups equipped with bi-invariant metrics

2022/07/26 by Jarek Kędra, Assaf Libman, Kędra, Jarek +1 · 1 citation
#math.GR #math.MG

paper · pdf · doi:10.48550/arxiv.2207.12704

Abstract

Given a bi-invariant metric on a group, we construct a version of an asymptotic cone without using ultrafilters. The new construction, called the directional asymptotic cone, is a contractible topological group equipped with a complete bi-invariant metric and admits a canonical Lipschitz homomorphism to the standard asymptotic cone. Moreover, the directional asymptotic cone of a countable group is separable.

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