Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
A new construction of CAT(0) cube complexes

### Robert Kropholler and Federico Vigolo

Algebraic & Geometric Topology 22 (2022) 3327–3375
##### Abstract

We introduce the notion of coupled link cube complexes (CLCCs) 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. 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.

##### Keywords
CAT(0), cube complex, link, hyperbolic group, cohomological dimension
##### Mathematical Subject Classification 2010
Primary: 20F65, 20F67, 20J05, 51M15, 57Q99