Elasticity of free type III actions of free groups

Antoine Poulin

Elasticity of free type III actions of free groups

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arxiv 2412.07047 v1 pith:ZI352H3A submitted 2024-12-09 math.GR math.DSmath.LO

Antoine Poulin This is my paper · ORCID

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keywords freetypegroupsactionsinducedsettingadditionalcharacterization

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abstract

We prove that measure-class-preserving non-amenable treeable equivalence relations of type III, meaning not preserving any equivalent $\sigma$-finite measure, are induced by free actions of non-abelian free groups of any given number of generators, including infinitely generated free groups, with the additional property that no ends of the induced Schreier graph are vanishing. This is done using a characterization of type III due to Hopf for transformations and Dang-Ngoc-Nghiem in general. This highlights the difference between the type III setting and the measure-preserving setting.

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Spectral Theory for Borel PMP Graphs
math.LO 2026-02 accept novelty 7.0 of 10

Spectral theory of adjacency and Laplacian operators yields new optimal bounds on approximate measurable chromatic numbers of graphings and a spectral criterion for a measurable Tutte condition.

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