Work

The Borel complexity of conjugacy for Cantor minimal systems

Year: 2026

Type: preprint

Abstract: We prove that conjugacy of minimal homeomorphisms of the Cantor space is Borel bireducible with isomorphism of countable graphs, answering the Cantor minimal case of a question of Foreman. We obtain the lower bound by encoding countably based profinite groups. Finite quotient homomorphisms are represented by factor maps between a common family of minimal subshifts. Amalgamation makes the resulting inverse limit independent, up to conjugacy, of the quotient presentation. Conversely, finite-stage factorization recovers the group from any conjugacy of these inverse limits.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.12031

Authors: Dai, Xinan, Deng, Wenhao, Shi, Yingdong, Wu, Tailin, Yang, Yuchen

Institution: Westlake University

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Westlake University, Fudan University, ShanghaiTech University, Department of Artificial Intelligence, Korea University

OpenAlex ID: W7212953379

Cites: 18

Cited by:

Related to: 10