Decomposition of Borel graphs and cohomology

2025/04/24 by Hiroki Ishikura, Ishikura, Hiroki · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2504.17831

openalex publication_date 2025/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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