Stable rank 2 reflexive sheaves on ... with large ...
In the paper we construct some stratifications of the space of monic polynomials in real and complex cases. These stratifications depend on properties of roots of the polynomials on some given semialgebraic subset of R or C. We prove differential triviality of these stratifications. In the real case the proof is based on properties of the action of the group of interval exchange transformations on the set of all monic polynomials of some given degree. Finally we compare stratifications corresponding...
Un feuilletage de codimension un sur une variété orientable est de Rolle s’il vérifie la propriété suivante : une courbe transverse à coupe au plus une fois chaque feuille. Soit une fonction tapissante sur , i.e. propre et possédant un nombre fini de valeurs critiques. Nous montrons que si l’ensemble des singularités de la restriction de aux feuilles de vérifie certaines propriétés de finitude, alors la restriction de au complémentaire d’un nombre fini de feuilles possède une structure...
Some properties of the range on an open leaf of some codimension-one foliation are shown. They are different from the known properties of the distance of leaves. They imply that leaf is of fibred type over a complete Riemannian manifold with boundary, as well that there exists some vector field on . If is parallel then is diffeomorphic to and has non-positive curvature.