A new construction of CAT(0) cube complexes

Kropholler, Robert; Vigolo, Federico

doi:10.2140/agt.2022.22.3327

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A new construction of CAT(0) cube complexes

Robert Kropholler and Federico Vigolo

Algebraic & Geometric Topology 22 (2022) 3327–3375

DOI: 10.2140/agt.2022.22.3327

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

Volume 22, issue 7 (2022)