A new construction of CAT(0) cube complexes
arXiv:1802.01885 · doi:10.2140/agt.2022.22.3327
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.
Major revision: the material was reorganized, the main results were improved; new results examples and questions were added. 9 figures, 33 pages