Measure expanding actions, expanders and warped cones
Geometric Topology
2021-01-13 v2 Metric Geometry
Abstract
We define a way of approximating actions on measure spaces using finite graphs; we then show that in quite general settings these graphs form a family of expanders if and only if the action is expanding in measure. This provides a somewhat unified approach to construct expanders. We also show that the graphs we obtain are uniformly quasi-isometric to the level sets of warped cones. This way we can also prove non-embeddability results for the latter and restate an old conjecture of Gamburd-Jakobson-Sarnak.
Cite
@article{arxiv.1610.05837,
title = {Measure expanding actions, expanders and warped cones},
author = {Federico Vigolo},
journal= {arXiv preprint arXiv:1610.05837},
year = {2021}
}
Comments
33 pages, made a number of improvements and corrections throughout. To appear in Transactions of the AMS