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arXiv · 2207.12704

Directional asymptotic cones of groups equipped with bi-invariant metrics

Jarek Kędra·Assaf Libman
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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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Jarek Kędra, Assaf Libman. 2022-07-26. Directional asymptotic cones of groups equipped with bi-invariant metrics. https://arxiv.org/abs/2207.12704

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