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October 9, 20250 citationsOpen Access

Anti-classification results for conjugacy of diffeomorphisms on manifolds

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BPBo Peng

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 (2025) studied this question.

synapsesocial.com/papers/68e8439a9989581a2fd4e031https://doi.org/10.48550/arxiv.2505.09491
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Also Consider

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  1. 1A classification of 5-dimensional manifolds, homogeneous souls of codimension two and non-diffeomorphic pairs2026
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  3. 3Classification of gradient-like flows without heteroclinic intersections on four-dimensional manifolds2026
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  5. 5Anti-classification results for weakly mixing diffeomorphisms2024