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.