An elementary approach to sofic groupoids

The variational principle of topological pressure for actions of sofic groupoids

This article establishes the variational principle of topological pressure for actions of sofic groupoids.

Entropy theory for sofic groupoids I: the foundations

This is the first part in a series in which sofic entropy theory is generalized to class-bijective extensions of sofic groupoids. Here we define topological and measure entropy and prove invariance. We also establish the variational principle, compute the entropy of Bernoulli shift actions and answer a question of Benjy Weiss pertaining to the isomorphism problem for non-free Bernoulli shifts. The proofs are independent of previous literature.

Sofic dimension for discrete measured groupoids

For discrete measured groupoids preserving a probability measure we introduce a notion of sofic dimension that measures the asymptotic growth of the number of sofic approximations on larger and larger finite sets. In the case of groups we give a formula for free products with amalgamation over an amenable subgroup. We also prove a free product formula for measure-preserving actions.

An elementary approach to sofic equivalence relations

We present an elementary description of sofic equivalence relations, as well as some permanence properties for soficity. We answer a question by Conley, Kechris and Tucker-Drob of determining soficity in terms of the full group for aperiodic relations.

几乎基本平展群胚

Almost elementary étale groupoids

本研究引入几乎基本性作为平展群胚的新有限逼近性质，证明极小几乎基本群胚的约化C*-代数为$\boldsymbol{\text{Z}}$-稳定，还探讨了其与群胚相关性质的联系。