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Displaying similar documents to “Foliations of M 3 defined by 2 -actions”

Smoothability of proper foliations

John Cantwell, Lawrence Conlon (1988)

Annales de l'institut Fourier

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Compact, C 2 -foliated manifolds of codimension one, having all leaves proper, are shown to be C -smoothable. More precisely, such a foliated manifold is homeomorphic to one of class C . The corresponding statement is false for foliations with nonproper leaves. In that case, there are topological distinctions between smoothness of class C r and of class C r + 1 for every nonnegative integer r .

Tischler fibrations of open foliated sets

John Cantwell, Lawrence Conlon (1981)

Annales de l'institut Fourier

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Let M be a closed, foliated manifold, and let U be an open, connected, saturated subset that is a union of locally dense leaves without holonomy. Supplementary conditions are given under which U admits an approximating (Tischler) fibration over S 1 . If the fibration exists, conditions under which the original leaves are regular coverings of the fibers are studied also. Examples are given to show that our supplementary conditions are generally required.