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A continuum of expanders

Volume 238 / 2017

David Hume Fundamenta Mathematicae 238 (2017), 143-152 MSC: Primary 20F65; Secondary 05C25. DOI: 10.4064/fm101-11-2016 Published online: 1 March 2017

Abstract

A regular equivalence between two graphs $\varGamma ,\varGamma ’$ is a pair of uniformly proper Lipschitz maps $V\varGamma \to V\varGamma ’$ and $V\varGamma ’\to V\varGamma $. Using separation profiles we prove that there are $2^{\aleph _0}$ regular equivalence classes of expander graphs, and of finitely generated groups with a representative which isometrically contains expanders.

Authors

  • David HumeMathematical Institute
    University of Oxford
    Woodstock Road
    Oxford, OX2 6GG, UK
    e-mail

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