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Stratifications of polynomial spaces

Lev Birbrair (1998)

Publicacions Matemàtiques

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...

Structure locale et globale des feuilletages de Rolle, un théorème de fibration

Frédéric Chazal (1998)

Annales de l'institut Fourier

Un feuilletage de codimension un sur une variété orientable M est de Rolle s’il vérifie la propriété suivante : une courbe transverse à coupe au plus une fois chaque feuille. Soit Q une fonction tapissante sur M , i.e. propre et possédant un nombre fini de valeurs critiques. Nous montrons que si l’ensemble des singularités de la restriction de Q aux feuilles de F vérifie certaines propriétés de finitude, alors la restriction de au complémentaire d’un nombre fini de feuilles possède une structure...

Structure of a leaf of some codimension one riemannian foliation

Krystyna Bugajska (1988)

Annales de l'institut Fourier

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 v on . If v is parallel then is diffeomorphic to ' × R and has non-positive curvature.

Subgroups of continuous groups acting differentiably on the half-line

Joseph F. Plante (1984)

Annales de l'institut Fourier

We consider groups of diffeomorphisms of the closed half-line which fix only the end point. When the group is a Lie group it is isomorphic to a subgroup of the affine group. On the other hand, when the group is isomorphic to a discrete subgroup of a solvable Lie group it is topologically equivalent to a subgroup of the affine group.

Submanifolds of codimension two and homology equivalent manifolds

Sylvain E. Cappell, Julius L. Shaneson (1973)

Annales de l'institut Fourier

In this paper new methods of studying codimension two embeddings of manifolds are outlined. Results are stated on geometric periodicity of knot cobordism. The group of local knots of a manifold in a 2-plane bundle is introduced and computed, and applied to C o -close embeddings. General codimension two splitting theorems are discussed, with applications to equivariant knots and knot cobordism. A general existence theorem for P.L. (non-locally flat) embeddings is also given.The methods involve some...

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