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arXiv · 2504.17831

Decomposition of Borel graphs and cohomology

Hiroki Ishikura
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Abstract

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.

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Hiroki Ishikura. 2025-04-24. Decomposition of Borel graphs and cohomology. https://arxiv.org/abs/2504.17831

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