Quasi-isometric groups with no common model geometry
Geometric Topology
2018-12-05 v2 Group Theory
Abstract
A simple surface amalgam is the union of a finite collection of surfaces with precisely one boundary component each and which have their boundary curves identified. We prove if two fundamental groups of simple surface amalgams act properly and cocompactly by isometries on the same proper geodesic metric space, then the groups are commensurable. Consequently, there are infinitely many fundamental groups of simple surface amalgams that are quasi-isometric, but which do not act properly and cocompactly on the same proper geodesic metric space.
Cite
@article{arxiv.1711.05026,
title = {Quasi-isometric groups with no common model geometry},
author = {Emily Stark and Daniel Woodhouse},
journal= {arXiv preprint arXiv:1711.05026},
year = {2018}
}
Comments
v2: 19 pages, 6 figures; minor changes. To appear in Journal of the London Mathematical Society