Quasi-isometries between groups with infinitely many ends
Geometric Topology
2007-05-23 v1
Abstract
Let G and F be finitely generated groups with infinitely many ends and let A and B be graph of groups decompositions of F and G such that all edge groups are finite and all vertex groups have at most one end. We show that G and F are quasi-isometric if and only if every one-ended vertex group of A is quasi-isometric to some one-ended vertex group of B and every one-ended vertex group of B is quasi-isometric to some one-ended vertex group of A. From our proof it also follows that if G is any finitely generated group, of order at least three, the groups: G*G, G*Z,G*G*G and G* Z/2Z are all quasi-isometric.
Cite
@article{arxiv.math/0405274,
title = {Quasi-isometries between groups with infinitely many ends},
author = {Panos Papazoglu and Kevin Whyte},
journal= {arXiv preprint arXiv:math/0405274},
year = {2007}
}