Group splittings and asymptotic topology
Group Theory
2016-09-07 v1
Abstract
It is a consequence of the theorem of Stallings on groups with many ends that splittings over finite groups are preserved by quasi-isometries. In this paper we use asymptotic topology to show that group splittings are preserved by quasi-isometries in many cases. Roughly speaking we show that splittings are preserved under quasi-isometries when the vertex groups are fundamental groups of aspherical manifolds (or more generally `coarse PD(n)-groups') and the edge groups are `smaller' than the vertex groups.
Cite
@article{arxiv.math/0201312,
title = {Group splittings and asymptotic topology},
author = {Panos Papasoglu},
journal= {arXiv preprint arXiv:math/0201312},
year = {2016}
}
Comments
14 pages