A continuum of expanders

2014/10/01 by Hume, David
#05C63 #20F65 #20F69 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1410.0246

Abstract

A regular equivalence between two graphs Γ,Γ' is a pair of uniformly proper Lipschitz maps VΓ→ VΓ' and VΓ'→ VΓ. Using separation profiles we prove that there are 2^ℵ₀ regular equivalence classes of expander graphs, and of finitely generated groups with a representative which isometrically contains expanders.

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