Displaying similar documents to “On some spaces which are covered by a product space”

Foliations with all leaves compact

D. B. A. Epstein (1976)

Annales de l'institut Fourier

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The notion of the “volume" of a leaf in a foliated space is defined. If L is a compact leaf, then any leaf entering a small neighbourhood of L either has a very large volume, or a volume which is approximatively an integral multiple of the volume of L . If all leaves are compact there are three related objects to study. Firstly the topology of the quotient space obtained by identifying each leaf to a point ; secondly the holonomy of a leaf ; and thirdly whether the leaves have a locally...

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.

Transversely homogeneous foliations

Robert A. Blumenthal (1979)

Annales de l'institut Fourier

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A foliation of a manifold is transversely homogeneous if it can be defined by local submersions to a homogeneous space G / K which on overlaps differ by translations. We explore the topology and geometry of such foliations and give a structure theorem for the case when K is compact. We investigate the relationship between the structure equations of G and the normal bundle of the foliation and provide a differential forms characterization of a large class of homogeneous foliations. As a special...

Pierrot's theorem for singular Riemannian foliations.

Robert A. Wolak (1994)

Publicacions Matemàtiques

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Let F be a singular Riemannian foliation on a compact connected Riemannian manifold M. We demonstrate that global foliated vector fields generate a distribution tangent to the strata defined by the closures of leaves of F and which, in each stratum, is transverse to these closures of leaves.

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 .