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arXiv · 2609.22416

Expanders prevent Property (H)

Bruno de Mendonç Braga·Chris Gartland·Gilles Lancien·Pavlos Motakis·Eva Pernecká·Thomas Schlumprecht
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Abstract

We show that if a sequence of expander graphs equi-coarsely embeds into a Banach space, then this Banach space fails Kasparov and Yu's Property (H). Consequently, no Banach space with Property (H) can be coarsely universal for all countable groups. We provide a Lean verification of our results.

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Bruno de Mendonç Braga, Chris Gartland, Gilles Lancien, Pavlos Motakis, Eva Pernecká, Thomas Schlumprecht. 2026-09-18. Expanders prevent Property (H). https://arxiv.org/abs/2609.22416

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