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This is a Quantitative Study study.

October 9, 2025Open Access

Anti-classification results for conjugacy of diffeomorphisms on manifolds

Key Points

The topological conjugacy relation of diffeomorphisms on manifolds of dimension at least 2 is not classifiable by countable structures.
This research provides a definitive answer to a question raised by Foreman and Gorodetski regarding conjugacy.
We demonstrate that $E_0$ can be reduced to the topological conjugacy relation of minimal diffeomorphisms on the 2-torus.
This work expands on previous findings by addressing another query posed by Foreman related to minimal diffeomorphisms.

Abstract

We show that the topological conjugacy relation of diffeomorphisms on any manifold of dimension at least 2 is not classifiable by countable structures. This answers a question of Foreman and Gorodetski. We also prove that E₀ is reducible into the topological conjugacy relation of minimal diffeomorphisms on the 2-torus, which answers a question of Foreman.

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Cite This Study

Bo Peng (Wed,) studied this question.

synapsesocial.com/papers/68e8439a9989581a2fd4e031 https://doi.org/https://doi.org/10.48550/arxiv.2505.09491

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