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Close cohomologous Morse forms with compact leaves

Irina Gelbukh (2013)

Czechoslovak Mathematical Journal

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 γ , then any close cohomologous form has a compact leave close to γ . 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...

Codimension one minimal foliations and the fundamental groups of leaves

Tomoo Yokoyama, Takashi Tsuboi (2008)

Annales de l’institut Fourier

Let ℱ be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold M . We show that if the fundamental group of each leaf of ℱ is isomorphic to Z , then ℱ is without holonomy. We also show that if π 2 ( M ) ≅ 0 and the fundamental group of each leaf of ℱ is isomorphic to Z k ( k ∈ Z ≥ 0 ), then ℱ is without holonomy.

Cohomology of Lie groups made discrete.

Pere Pascual Gainza (1990)

Publicacions Matemàtiques

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.

Combinatoire des simplexes sans singularités I. Le cas différentiable

Jean Cerf (1998)

Annales de l'institut Fourier

On définit le bicomplexe C • , • , extension naturelle du complexe C engendré par un ensemble simplicial Γ . Ceci permet de définir la notion de ruban de base un cycle de C . La somme directe de l’homologie des colonnes de C • , • contient, outre l’homologie de C , des groupes dans lesquels se trouvent les obstructions à l’existence de rubans. Si Γ 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...

Conformal curvature for the normal bundle of a conformal foliation

Angel Montesinos (1982)

Annales de l'institut Fourier

It is proved that the normal bundle ℋ of a distribution 𝒱 on a riemannian manifold admits a conformal curvature C if and only if 𝒱 is a conformal foliation. Then ℋ is conformally flat if and only if C vanishes. Also, the Pontrjagin classes of ℋ can be expressed in terms of C .

Connected components of the strata of the moduli spaces of quadratic differentials

Erwan Lanneau (2008)

Annales scientifiques de l'École Normale Supérieure

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...

Currently displaying 61 – 80 of 438