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A cubical Rips construction

Macarena Arenas

Algebraic & Geometric Topology 24 (2024) 4353–4372
Abstract

Given a finitely presented group Q and a compact special cube complex X with nonelementary hyperbolic fundamental group, we produce a nonelementary torsion-free cocompactly cubulated hyperbolic group Γ that surjects onto Q, with kernel isomorphic to a quotient of G = π1 X and such that max {cd (G),2} cd (Γ) cd (G) 1.

Keywords
small cancellation, cube complexes, hyperbolic groups
Mathematical Subject Classification
Primary: 20F06, 20F67
References
Publication
Received: 4 May 2022
Revised: 17 January 2023
Accepted: 8 February 2023
Published: 17 December 2024
Authors
Macarena Arenas
DPMMS, Centre for Mathematical Sciences
University of Cambridge
Cambridge
United Kingdom

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