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Leighton's theorem:
Extensions, limitations and quasitrees
Martin R Bridson and Sam Shepherd |
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Algebraic & Geometric Topology 22 (2022) 881–917
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Abstract |
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Leighton’s theorem states that if there is a tree that covers two finite graphs and , then there is a finite graph that is covered by and covers both and . We prove that this result does not extend to regular covers by graphs other than trees. Nor does it extend to nonregular covers by a quasitree, even if the automorphism group of the quasitree contains a uniform lattice. But it does extend to regular coverings by quasitrees. |
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Keywords
quasitrees, covering spaces, Leighton's theorem
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Mathematical Subject Classification
Primary: 05C25, 20F65, 20F67
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References |
Publication
Received: 9 September 2020
Revised: 13 January 2021
Accepted: 1 February 2021
Published: 3 August 2022
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Authors |
| Martin R Bridson | |
| Mathematical Institute University of Oxford Oxford United Kingdom |
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| Sam Shepherd | |
| Department of Mathematics Vanderbilt University Nashville, TN United States |
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