Les inégalités de Morse
Nous construisons sur l’ensemble des feuilletages (avec singulariés) d’un espace analytique compact normal une structure analytique complexe. Dans le cas faiblement kählérien, nous montrons qu’à un point frontière de la compactification naturelle de l’espace des feuilletages est encore associé un feuilletage.
The main result is a Pursell-Shanks type theorem for codimension one foliations. This theorem can be viewed as a partial solution of a hypothetical general version of the theorem of Pursell-Shanks. Several propositions and lemmas on foliations are contained in the proof.
We prove that on a -complex the obstruction for a line bundle to be the fractional power of a suitable pullback of the Hopf bundle on a 2-dimensional sphere is the vanishing of the square of the first Chern class of . On the other hand we show that if one looks at integral powers then further secondary obstructions exist.
We exhibit a six dimensional manifold with a line bundle on it which is not the pullback of a bundle on .
We study secondary obstructions to representing a line bundle as the pull-back of a line bundle on and we interpret them geometrically.
In this paper we study the geometry of direct connections in smooth vector bundles (see N. Teleman [Tn.3]); we show that the infinitesimal part, , of a direct connection τ is a linear connection. We determine the curvature tensor of the associated linear connection As an application of these results, we present a direct proof of N. Teleman’s Theorem 6.2 [Tn.3], which shows that it is possible to represent the Chern character of smooth vector bundles as the periodic cyclic homology class of a...