Research reveals that conjugacy of diffeomorphisms on manifolds isn't classifiable by countable structures, suggesting deeper complexity.
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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Bo Peng (2025) studied this question.
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