Let be a compact oriented 3-manifold whose boundary contains a single torus and let be a taut foliation on whose restriction to has a Reeb component. The main technical result of the paper, asserts that if is obtained by Dehn filling along any curve not parallel to the Reeb component, then has a taut foliation.
We show that any transversally complete Riemannian foliation of dimension one on any possibly non-compact manifold is tense; namely, admits a Riemannian metric such that the mean curvature form of is basic. This is a partial generalization of a result of Domínguez, which says that any Riemannian foliation on any compact manifold is tense. Our proof is based on some results of Molino and Sergiescu, and it is simpler than the original proof by Domínguez. As an application, we generalize some...
We study the cohomology properties of the singular foliation ℱ determined by an action Φ: G × M → M where the abelian Lie group G preserves a riemannian metric on the compact manifold M. More precisely, we prove that the basic intersection cohomology is finite-dimensional and satisfies the Poincaré duality. This duality includes two well known situations: ∙ Poincaré duality for basic cohomology (the action Φ is almost free). ∙ Poincaré duality for intersection cohomology (the group G is compact...
We describe explicitly the group of transverse diffeomorphisms of several types of minimal linear foliations on the torus , . We show in particular that non-quadratic foliations are rigid, in the sense that their only transverse diffeomorphisms are and translations. The description derives from a general formula valid for the group of transverse diffeomorphisms of any minimal Lie foliation on a compact manifold. Our results generalize those of P. Donato and P. Iglesias for , P. Iglesias and...
The definition of a Stefan suspension of a diffeomorphism is given. If is the Stefan suspension of the diffeomorphism g over a Stefan foliation , and G₀ ∈ satisfies the condition , then we compute the *-holonomy group for the leaf determined by G₀. A representative element of the *-holonomy along the standard imbedding of S¹ into F₀ is characterized. A corollary for the case when G₀ contains only one point is derived.
Foliations on the 2-sphere with a finite number of non-orientable singularities are considered. For this class a Poincaré-Bendixson theorem is established. In particular, the work gives an answer to a problem of H. Rosenberg concerning labyrinths.
On introduit, dans ce travail, une hypothèse sur le spiralement d’une feuille d’un feuilletage analytique réel de codimension un (hypersurface pfaffienne). On en tire des résultats très généraux de finitude du type de Khovanskii. Des exemples précis montrent la généralité de ces hypersurfaces pfaffiennes. Une description complété des bouts de telles variétés en dimension trois est donnée.
Soit un feuilletage riemannien sur une variété compacte; est le feuilletage singulier défini par les adhérences des feuilles le feuilletage induit sur une adhérence générique. On étudie le cas où n’a pas de champ transverse non trivial. Alors l’espace quotient a une structure naturelle de variété de Sataké, de manière que la projection soit un morphisme (de variétés de Sataké) avec pliage autour des adhérences singulières.