High-dimensional expansion and soficity of groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909139117015040 |
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| author | Gohla, Lukas Thom, Andreas |
| author_facet | Gohla, Lukas Thom, Andreas |
| contents | For $d \geq 4$ and $p$ a sufficiently large prime, we construct a lattice $Γ\leq {\rm PSp}_{2d}(\mathbb Q_p),$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09582 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-dimensional expansion and soficity of groups Gohla, Lukas Thom, Andreas Group Theory For $d \geq 4$ and $p$ a sufficiently large prime, we construct a lattice $Γ\leq {\rm PSp}_{2d}(\mathbb Q_p),$ 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. |
| title | High-dimensional expansion and soficity of groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2403.09582 |