On transverse foliations

Atsushi Sato; Itiro Tamura

Displaying similar documents to “On transverse foliations”

A foliation of $𝐑^{3}$ and other punctured 3-manifolds by circles

Elmar Vogt (1989)

Publications Mathématiques de l'IHÉS

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A note on codimension-1 foliations

Carlo Petronio (1999)

Rendiconti del Seminario Matematico della Università di Padova

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Foliations with few non-compact leaves.

Vogt, Elmar (2002)

Algebraic & Geometric Topology

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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.

On G-foliations

Robert Wolak (1985)

Annales Polonici Mathematici

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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.

$R$ -covered foliations of hyperbolic 3-manifolds.

Calegari, Danny (1999)

Geometry & Topology

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Limit sets of foliations

Richard Sacksteder, Art J. Schwartz (1965)

Annales de l'institut Fourier

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Soit $V$ une variété munie d’une structure feuilletée de co-dimension un. On démontre plusieurs théorème relatifs à des conditions entraînant que le groupe d’holonomie et le pseudo-groupe d’holonomie d’une certaine feuille $F \subset V$ est infini.