Displaying similar documents to “Every orientable 3-manifold is a B Γ .”

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 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.

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 .