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We study the topology of foliations of close cohomologous Morse forms (smooth closed 1-forms with non-degenerate singularities) on a smooth closed oriented manifold. We show that if a closed form has a compact leave , then any close cohomologous form has a compact leave close to . Then we prove that the set of Morse forms with compactifiable foliations (foliations with no locally dense leaves) is open in a cohomology class, and the number of homologically independent compact leaves does not decrease...
Let be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold . We show that if the fundamental group of each leaf of is isomorphic to , then is without holonomy. We also show that if and the fundamental group of each leaf of is isomorphic to (), then is without holonomy.
Nous démontrons des théorèmes de dualité de Poincaré et de de Rham pour la cohomologie basique et l’homologie des courants transverses invariants d’un feuilletage riemannien.
We give a survey of the work of Milnor, Friedlander, Mislin, Suslin and other authors on the Friedlander-Milnor conjecture on the homology of Lie groups made discrete and its relation to the algebraic K-theory of fields.
On définit le bicomplexe , extension naturelle du complexe engendré par un ensemble simplicial . Ceci permet de définir la notion de ruban de base un cycle de . La somme directe de l’homologie des colonnes de contient, outre l’homologie de , des groupes dans lesquels se trouvent les obstructions à l’existence de rubans. Si est un sous-ensemble simplicial, stable par subdivision, de l’ensemble des simplexes singuliers d’un espace topologique, l’existence de rubans entraîne l’invariance...
It is proved that the normal bundle of a distribution on a riemannian manifold admits a conformal curvature if and only if is a conformal foliation. Then is conformally flat if and only if vanishes. Also, the Pontrjagin classes of can be expressed in terms of .
In two fundamental classical papers, Masur [14] and Veech [21] have independently proved that the Teichmüller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore interesting to have a classification of the ergodic components. Veech has proved that these strata are not necessarily connected. In a recent work [8], Kontsevich and Zorich have completely classified the components in the particular case where the quadratic...
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