Iterated asymptotic cones
Metric Geometry
2011-08-05 v1 Group Theory
Abstract
Iterated asymptotic cones have been used by Dru\c{t}u and Sapir to construct a group with uncountably many pairwise non-homeomorphic asymptotic cones. In this paper we define a class of metric spaces which display a wide range of behaviors with respect to iterated asymptotic cones, and we use those to construct examples within the class of groups. Namely, we will show that there exists a group whose iterated cones are pairwise non-homeomorphic, or periodically homeomorphic.
Cite
@article{arxiv.1108.1146,
title = {Iterated asymptotic cones},
author = {Lars Scheele and Alessandro Sisto},
journal= {arXiv preprint arXiv:1108.1146},
year = {2011}
}