Decomposition of Borel graphs and cohomology
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914385388109824 |
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| author | Ishikura, Hiroki |
| author_facet | Ishikura, Hiroki |
| contents | We give a cohomological criterion for certain decomposition of Borel graphs, which is an analog of Dunwoody's work on accessibility of groups. As an application, we prove that a Borel graph $(X,G)$ with uniformly bounded degrees of cohomological dimension one is Lipschitz equivalent to a Borel acyclic graph on $X$. This gives a new proof of a result of Chen-Poulin-Tao-Tserunyan on Borel graphs with components quasi-isometric to trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17831 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decomposition of Borel graphs and cohomology Ishikura, Hiroki Group Theory Dynamical Systems Logic We give a cohomological criterion for certain decomposition of Borel graphs, which is an analog of Dunwoody's work on accessibility of groups. As an application, we prove that a Borel graph $(X,G)$ with uniformly bounded degrees of cohomological dimension one is Lipschitz equivalent to a Borel acyclic graph on $X$. This gives a new proof of a result of Chen-Poulin-Tao-Tserunyan on Borel graphs with components quasi-isometric to trees. |
| title | Decomposition of Borel graphs and cohomology |
| topic | Group Theory Dynamical Systems Logic |
| url | https://arxiv.org/abs/2504.17831 |