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 that surjects onto Q, with kernel isomorphic to a quotient of G=π1 X and such that max\cd(G),2\≥ cd()≥ cd(G)-1.
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