Separable and tree-like asymptotic cones of groups
Metric Geometry
2011-03-08 v2 Group Theory
Logic
Abstract
Using methods from nonstandard analysis, we will discuss which metric spaces can be realized as asymptotic cones. Applying the results we will find in the context of groups, we will prove that a group with "a few" separable asymptotic cones is virtually nilpotent, and we will classify the real trees appearing as asymptotic cones of (not necessarily hyperbolic) groups.
Cite
@article{arxiv.1010.1199,
title = {Separable and tree-like asymptotic cones of groups},
author = {Alessandro Sisto},
journal= {arXiv preprint arXiv:1010.1199},
year = {2011}
}
Comments
The hypothesis of Theorem 1.2 had to be strengthened