Revisiting Leighton's Theorem with the Haar Measure
Group Theory
2018-07-31 v2 Geometric Topology
Abstract
Leighton's graph covering theorem states that a pair of finite graphs with isomorphic universal covers have a common finite cover. We provide a new proof of Leighton's theorem that allows generalizations; we prove the corresponding result for graphs with fins. As a corollary we obtain pattern rigidity for free groups with line patterns, building on the work of Cashen-Macura and Hagen-Touikan. To illustrate the potential for future applications, we give a quasi-isometric rigidity result for a family of cyclic doubles of free groups.
Cite
@article{arxiv.1806.08196,
title = {Revisiting Leighton's Theorem with the Haar Measure},
author = {Daniel J. Woodhouse},
journal= {arXiv preprint arXiv:1806.08196},
year = {2018}
}
Comments
9 pages, 2 figures. Introduction adjusted. A new qi-rigidity application is added