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Directional asymptotic cones of groups equipped with bi-invariant metrics (2207.12704v2)
Published 26 Jul 2022 in math.GR and math.MG
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.