High-dimensional expansion and soficity of groups

2024/03/14 by Lukas Gohla, Andreas Thom, Gohla, Lukas +1 · 4 citations
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Graph theory and applications #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2403.09582

openalex publication_date 2024/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For d ≥ 4 and p a sufficiently large prime, we construct a lattice Γ≤ \rm PSp_2d(\mathbb Q_p), such that its universal central extension cannot be sofic if Γ satisfies some weak form of stability in permutations. In the proof, we make use of high-dimensional expansion phenomena and, extending results of Lubotzky, we construct new examples of cosystolic expanders over arbitrary finite abelian groups.

Cited by

• Remarks on approximability and stability for groups
• On L¹-approximation of groups
• Minor-excluded graphs and soficity
• Non-uniform higher-rank lattices are character rigid

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