A new construction of CAT(0) cube complexes
Metric Geometry
2023-02-15 v2 Group Theory
Abstract
We introduce the notion of coupled link cube complex (CLCC) as a means of constructing interesting cocompactly cubulated groups. CLCCs are defined locally, making them a useful tool when precise control over the links is required. In this paper we study some general properties of CLCCs, such as their (co)homological dimension and criteria for hyperbolicity. Some examples of fundamental groups of CLCCs are RAAGs, RACGs, surface groups and some manifold groups. As immediate applications of our criteria we produce a number of cubulated 3 and 4 manifolds with hyperbolic fundamental group.
Cite
@article{arxiv.1802.01885,
title = {A new construction of CAT(0) cube complexes},
author = {Robert Kropholler and Federico Vigolo},
journal= {arXiv preprint arXiv:1802.01885},
year = {2023}
}
Comments
Major revision: the material was reorganized, the main results were improved; new results examples and questions were added. 9 figures, 33 pages