Displaying similar documents to “Foliations and spinnable structures on manifolds”

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 .

Taut foliations of 3-manifolds and suspensions of S 1

David Gabai (1992)

Annales de l'institut Fourier

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Let M be a compact oriented 3-manifold whose boundary contains a single torus P and let ℱ be a taut foliation on M whose restriction to ∂ M has a Reeb component. The main technical result of the paper, asserts that if N is obtained by Dehn filling P along any curve not parallel to the Reeb component, then N has a taut foliation.

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.

Extending regular foliations

J. W. Smith (1969)

Annales de l'institut Fourier

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A p -dimensional foliation F on a differentiable manifold M is said to extend provided there exists a ( p + 1 ) -dimensional foliation F ' on M with F ⊂ F ' . Our main result asserts that if M and F extends over relatively compact subsets of M .