Stability, approximable quotients, and higher property (T)

2025/12/09 by Francesco Fournier-Facio, Fournier-Facio, Francesco
Mathematics · #FOS: Mathematics #Functional Equations Stability Results #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2512.09180

openalex publication_date 2025/12/09 · openalex created_date 2025/12/12 · openalex updated_date 2026/08/01

Abstract

We construct a wealth of groups that are finitely presented, Frobenius stable, have property (T), but are very far from having property (T₂). Our method also shows that property (T₂) does not pass to quotients. A post-scriptum relates and comments on an experience this paper had with an AI benchmark.

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Cited by

• Higher property T and below-rank phenomena of lattices

Related

• A Cup Product Obstruction to Frobenius Stability
• On stable quotients
• Stable Elements and Property (S)
• Stability, cohomology vanishing, and non-approximable groups
• Higher property T and below-rank phenomena of lattices