Journal article
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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Authors
Bibliographic Details
- Publisher:
- Cambridge University Press Publisher's website
- Journal:
- Mathematical Proceedings of the Cambridge Philosophical Society Journal website
- 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
Item Description
- Language:
- English
- Keywords:
- Pubs id:
-
1086961
- Local pid:
- pubs:1086961
- Deposit date:
- 2020-11-05
Terms of use
- Copyright holder:
- Cambridge Philosophical Society
- Copyright date:
- 2019
- Rights statement:
- © Cambridge Philosophical Society 2020.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Cambridge University Press at: https://doi.org/10.1017/S0305004119000550
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