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arXiv · 1806.08196

Revisiting Leighton's Theorem with the Haar Measure

Daniel J. Woodhouse
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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 generalizations; 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.

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Daniel J. Woodhouse. 2018-06-21. Revisiting Leighton's Theorem with the Haar Measure. https://arxiv.org/abs/1806.08196

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