A cubical Rips construction

Abstract

Given a finitely presented group $Q$ and a compact special cube complex $X$ with non-elementary hyperbolic fundamental group, we produce a non-elementary, torsion-free, cocompactly cubulated hyperbolic group $\Gamma$ that surjects onto $Q$, with kernel isomorphic to a quotient of $G={\pi }_{1}X$ and such that $max\{cd(G),2\}\ge cd(\Gamma )\ge cd(G)-1$.

Version 2: 21 pages, 1 figure, implemented referee's comments, accepted for publication at Algebraic & Geometric Topology

References in corpus (3)

• Criteria for virtual fibering
• Cohomology of group theoretic Dehn fillings I: Cohen-Lyndon type theorems
• Super-exponential distortion of subgroups of CAT(-1) groups