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Mathematical Proceedings of the Cambridge Philosophical Society Mathematical Proceedings of the Cambridge Philosophical Society

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Small non-Leighton two-complexes

Part of: Special aspects of infinite or finite groups Graph theory

Published online by Cambridge University Press:  05 September 2022

NATALIA S. DERGACHEVA  and
ANTON A. KLYACHKO
NATALIA S. DERGACHEVA
Affiliation:
Faculty of Mechanics and Mathematics of Moscow State University,Moscow 119991, Leninskie gory, MSU, Moscow, Russia. and Moscow Center for Fundamental and Applied Mathematics e-mails: nataliya.dergacheva@gmail.com, klyachko@mech.math.msu.su
ANTON A. KLYACHKO
Affiliation:
Faculty of Mechanics and Mathematics of Moscow State University,Moscow 119991, Leninskie gory, MSU, Moscow, Russia. and Moscow Center for Fundamental and Applied Mathematics e-mails: nataliya.dergacheva@gmail.com, klyachko@mech.math.msu.su
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Abstract

How many 2-cells must two finite CW-complexes have to admit a common, but not finite common, covering? Leighton’s theorem says that both complexes must have 2-cells. We construct an almost (?) minimal example with two 2-cells in each complex.

MSC classification

Secondary: 20F05: Generators, relations, and presentations 05C65: Hypergraphs 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , First View , pp. 1 - 7
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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Footnotes

†

This work was supported by the Russian Science Foundation, project no. 22-11-00075.

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