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High-dimensional expansion and soficity of groups

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arxiv 2403.09582 v2 pith:C5NU33L6 submitted 2024-03-14 math.GR

Lukas Gohla , Andreas Thom This is my paper · ORCID
classification math.GR
keywords constructexpansiongammagroupshigh-dimensionalabelianarbitrarycannot
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abstract

For $d \geq 4$ and $p$ a sufficiently large prime, we construct a lattice $\Gamma \leq {\rm PSp}_{2d}(\mathbb Q_p),$ such that its universal central extension cannot be sofic if $\Gamma$ 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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Non-uniform higher-rank lattices are character rigid

    math.GR 2025-07 accept novelty 8.0 of 10

    Every irreducible non-uniform lattice in a higher-rank semisimple group of characteristic not 2 is character rigid.

  2. Centralizers of sofic approximations of Kazhdan groups

    math.GR 2026-08 conditional novelty 7.0 of 10

    A Kazhdan group with a sofic embedding having an ergodic centralizer is LEF; finitely presented examples are residually finite.

  3. Hyperlinearity, stability and asymptotic spectral gap of higher rank lattices

    math.GR 2025-06 conditional novelty 7.0 of 10

    For higher-rank lattices, Hilbert-Schmidt stability implies non-hyperlinearity of certain central extensions, and character rigidity is equivalent to hyperfinite Hilbert-Schmidt stability.

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