Cubical small-cancellation theory and large-dimensional hyperbolic groups

Given a finitely presented group Q and a compact special cube complex X with nonelementary hyperbolic fundamental group, we produce a non-elementary, torsion-free, cocompactly cubulated hyperbolic group Γ that surjects onto Q, with kernel isomorphic to a quotient of G = π_1X and such that max{cd(G),2} ≥ cd(Γ) ≥ cd(G)−1. Separately, we show that under suitable hypotheses, the second homotopy group of the coned-off space associated to a C(9) cubical presentation is trivial, and use this to provide classifying spaces for proper actions for the fundamental groups of many quotients of square complexes admitting such cubical presentations. When the cubical presentations satisfy a condition analogous to requiring that the relators in a group presentation are not proper powers, we conclude that the corresponding coned-off space is aspherical.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2023

Author dc:creator

• Arenas, Macarena

Advisor dc:contributor.advisor

• Wilton, Henry

• hyperbolic groups
• cube complexes
• small-cancellation theory

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/1915c927-9913-48ee-a6af-b0b15e6f08b3/download
• https://creativecommons.org/licenses/by/4.0/

Language dc:language

eng

Author Identifier

0000-0003-4965-8121

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/357537