2 papers
math.CO2026
Tracks on planar complexes and soficity
Hiroki Ishikura
We show that every probability-measure-preserving equivalence relation generated by a locally-finite Borel graph with planar connected components is sofic in the sense of Elek--Lip…
math.GR2026
Decomposition of Borel graphs and cohomology
Hiroki Ishikura
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 Bo…