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Revisiting Leighton's theorem with the Haar measure

Abstract:
Leighton’s graph covering theorem states that a pair of finite graphs with isomorphic universal covers have a common finite cover. We provide a new proof of Leighton’s theorem that allows generalisations; we prove the corresponding result for graphs with fins. As a corollary we obtain pattern rigidity for free groups with line patterns, building on the work of Cashen–Macura and Hagen–Touikan. To illustrate the potential for future applications, we give a quasi-isometric rigidity result for a family of cyclic doubles of free groups.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1017/S0305004119000550

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Cambridge University Press
Journal:
Mathematical Proceedings of the Cambridge Philosophical Society More from this journal
Volume:
170
Issue:
3
Article number:
615-623
Publication date:
2020-01-13
Acceptance date:
2019-10-29
DOI:
EISSN:
1469-8064
ISSN:
0305-0041
Language:
English
Keywords:
Pubs id:
1086961
Local pid:
pubs:1086961
Deposit date:
2020-11-05

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