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arXiv · 2607.20273

A Product-Neighbourhood Criterion for Fixed Price One

Raz Slutsky
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Abstract

We prove a flexible criterion for fixed price one, applying in particular to higher-rank lattices over local fields and automorphism groups of affine buildings, including lattices in exotic buildings. It also recovers fixed price one for amenable groups. We then establish a locally compact version, and deduce that every product of two noncompact, compactly generated, unimodular locally compact groups, as well as every lattice in such a product, has fixed price one.

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Raz Slutsky. 2026-07-22. A Product-Neighbourhood Criterion for Fixed Price One. https://arxiv.org/abs/2607.20273

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