Due to Epstain, if two homeomorphisms $f_0, f_1$ of a closed two-dimensional manifold $S$ are homotopic then they are isotopic. I've heard, that if $f_0, f_1$ are diffeomorphisms then the isotopy can be smoothed, that is $f_0, f_1$ are also diffeotopic. But I cannot find a link to this fact. I will very appretiate if somebody let me know where it is written. Only one paper I've manage to find is https://arxiv.org/abs/0908.2221, but there the case when $S$ is torus is exepted. What can be wrong for torus?
2026-03-25 12:15:27.1774440927
Isotopic diffeomorphisms of surface are diffeotopic?
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