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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
References
Publication
Received: 9 January 2020
Revised: 26 February 2021
Accepted: 5 October 2021
Published: 30 January 2023
Authors
Robert Kropholler
Mathematics Institute
University of Warwick
Coventry
United Kingdom
Federico Vigolo
Mathematisches Institut
Universität Münster
Münster
Germany