Localization of basic characteristic classes

Dirk Töben

Displaying similar documents to “Localization of basic characteristic classes”

On riemannian foliations with minimal leaves

Jesús A. Alvarez Lopez (1990)

Annales de l'institut Fourier

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For a Riemannian foliation, the topology of the corresponding spectral sequence is used to characterize the existence of a bundle-like metric such that the leaves are minimal submanifolds. When the codimension is $\leq 2$ , a simple characterization of this geometrical property is proved.

A few remarks on the geometry of the space of leaf closures of a Riemannian foliation

Małgorzata Józefowicz, R. Wolak (2007)

Banach Center Publications

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The space of the closures of leaves of a Riemannian foliation is a nice topological space, a stratified singular space which can be topologically embedded in $ℝ^{k}$ for k sufficiently large. In the case of Orbit Like Foliations (OLF) the smooth structure induced by the embedding and the smooth structure defined by basic functions is the same. We study geometric structures adapted to the foliation and present conditions which assure that the given structure descends to the leaf closure space....

Foliated G-structures and riemannian foliations.

Robert A. Wolak (1990)

Manuscripta mathematica

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Leaves of foliations with a transverse geometric structure of finite type.

Robert A. Wolak (1989)

Publicacions Matemàtiques

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In this short note we find some conditions which ensure that a G foliation of finite type with all leaves compact is a Riemannian foliation of equivalently the space of leaves of such a foliation is a Satake manifold. A particular attention is paid to transversaly affine foliations. We present several conditions which ensure completeness of such foliations.

On G-foliations

Robert Wolak (1985)

Annales Polonici Mathematici

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Some properties of foliations

Richard Sacksteder (1964)

Annales de l'institut Fourier

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De Rham decomposition theorems for foliated manifolds

Robert A. Blumenthal, James J. Hebda (1983)

Annales de l'institut Fourier

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We prove that if $M$ is a complete simply connected Riemannian manifold and $F$ is a totally geodesic foliation of $M$ with integrable normal bundle, then $M$ is topologically a product and the two foliations are the product foliations. We also prove a decomposition theorem for Riemannian foliations and a structure theorem for Riemannian foliations with recurrent curvature.

Unique Ergodicity for Foliations

Rufus Bowen (1975)

Publications mathématiques et informatique de Rennes

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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 $C^{\infty}$ -smoothable. More precisely, such a foliated manifold is homeomorphic to one of class $C^{\infty}$ . 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 $\partial M$ 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.