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Ainu
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A question about regularity of foliations

Let $F$ be a smooth foliation of a torus. Assume that $F$ can be mapped by a homeomorphism to an irrational-straight-line foliation $L$. Does it follow that $F$ can be mapped to $L$ by a diffeomorphism?

I am interested in 2 dimensional case and higher dimensional case.

Ainu
  • 105
  • 5