Borel complexity for product of trees and commuting partial maps

Koichi Oyakawa

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arXiv · 2609.34068

Borel complexity for product of trees and commuting partial maps

Koichi Oyakawa

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Abstract

We prove that every acylindrical action on uniformly locally finite product of trees induces the hyperfinite orbit equivalence relation on the Roller boundary. As a byproduct, we construct an example of a standard Borel space and two commuting bounded-to-one surjective partial Borel maps that generate a universal countable Borel equivalence relation. This contrasts to Shinko-Weilacher-Yu's theorem on hyperfiniteness of bounded-to-one actions of commutative monoids.

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Koichi Oyakawa. 2026-09-28. Borel complexity for product of trees and commuting partial maps. https://arxiv.org/abs/2609.34068

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