A continuum of expanders
Volume 238 / 2017
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.
