No quasi-isometric rigidity for proper actions on CAT(0) cube complexes
Group Theory
2023-05-10 v3
Abstract
We exhibit a variety of groups that act properly and even cocompactly on median graphs (a.k.a. one-skeletons of CAT(0) cube complexes), with quasi-isometric groups that do not admit any proper action on a median graph. This answes a question of Niblo, Sageev and Wise. Our examples are all quasi-isometrically trivial central extensions of certain cubulated groups.
Cite
@article{arxiv.2208.07102,
title = {No quasi-isometric rigidity for proper actions on CAT(0) cube complexes},
author = {Francesco Fournier-Facio and Anthony Genevois},
journal= {arXiv preprint arXiv:2208.07102},
year = {2023}
}
Comments
13 pages. v2: introduction slightly rewritten, with added references. v3: final version. To appear in Proceedings of the AMS