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Ainu
Ainu
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Let $F$ be a smooth foliation of a torus. It is knownAssume that $F$ can be mapped by a homeomorphism to aan 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.

Let $F$ be a smooth foliation of a torus. It is known that $F$ can be mapped by a homeomorphism to a 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.

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.

Source Link
Ainu
Ainu
  • 105
  • 5

A question about regularity of foliations

Let $F$ be a smooth foliation of a torus. It is known that $F$ can be mapped by a homeomorphism to a 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.