Straightening warped cones
Metric Geometry
2022-05-17 v3 Dynamical Systems
Group Theory
Abstract
We provide the converses to two results of J. Roe (Geom. Topol. 2005): first, the warped cone associated to a free action of an a-T-menable group admits a fibred coarse embedding into a Hilbert space, and second, a free action yielding a warped cone with property A must be amenable. We construct examples showing that in both cases the freeness assumption is necessary. The first equivalence is obtained also for other classes of Banach spaces, in particular for -spaces.
Cite
@article{arxiv.1705.06725,
title = {Straightening warped cones},
author = {Damian Sawicki and Jianchao Wu},
journal= {arXiv preprint arXiv:1705.06725},
year = {2022}
}
Comments
Final authors' version of the article published by JTA. Changes since v2: the proof of Lem. 3.8 (now Prop. 3.10) is split between several lemmata, the proof of Thm 4.2 simplified and more detailed