Cocycle stability in permutations of random simplicial complexes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908694647668736 |
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| author | Chapman, Michael Peled, Yuval |
| author_facet | Chapman, Michael Peled, Yuval |
| contents | Finding a non-sofic hyperbolic group will resolve two major problems in geometric group theory: Are there non sofic groups? Are there non residually finite hyperbolic groups?
In this paper, we propose a new probabilistic approach to this problem, based on the cocycle stability in permutations of random 2-dimensional Linial-Meshulam complexes. Specifically, we study their cocycle stability rate, which measures how far cochains with small coboundaries are from being cocycles.
Our main contribution is the following: If, in a middle triangle density range, these random complexes typically have a linear cocycle stability rate, then there exists a non-sofic hyperbolic group. Our proof method is inspired by a well known fact about the non local testability of Sipser-Spielman expander codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21566 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cocycle stability in permutations of random simplicial complexes Chapman, Michael Peled, Yuval Group Theory Combinatorics Finding a non-sofic hyperbolic group will resolve two major problems in geometric group theory: Are there non sofic groups? Are there non residually finite hyperbolic groups? In this paper, we propose a new probabilistic approach to this problem, based on the cocycle stability in permutations of random 2-dimensional Linial-Meshulam complexes. Specifically, we study their cocycle stability rate, which measures how far cochains with small coboundaries are from being cocycles. Our main contribution is the following: If, in a middle triangle density range, these random complexes typically have a linear cocycle stability rate, then there exists a non-sofic hyperbolic group. Our proof method is inspired by a well known fact about the non local testability of Sipser-Spielman expander codes. |
| title | Cocycle stability in permutations of random simplicial complexes |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2509.21566 |