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Leighton's theorem and regular cube complexes

Daniel J Woodhouse

Algebraic & Geometric Topology 23 (2023) 3395–3415
Abstract

Leighton’s graph covering theorem states that two finite graphs with common universal cover have a common finite cover. We generalize this to a large family of nonpositively curved special cube complexes that form a natural generalization of regular graphs. This family includes both hyperbolic and nonhyperbolic CAT(0) cube complexes.

Keywords
CAT(0) cube complexes, finite covering spaces
Mathematical Subject Classification
Primary: 20F65, 20F67
Secondary: 20E26, 20E42, 20F55
References
Publication
Received: 14 February 2022
Revised: 28 April 2022
Accepted: 19 May 2022
Published: 26 September 2023
Authors
Daniel J Woodhouse
University of Oxford
Oxford
United Kingdom
http://www.djwoodhouse.com

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