We will consider codimension one holomorphic foliations represented by sections , and having a compact Kupka component . We show that the Chern classes of the tangent bundle of behave like Chern classes of a complete intersection 0 and, as a corollary we prove that is a complete intersection in some cases.
Motivated by the work of A. C. Naolekar and A. S. Thakur (2014) we introduce notions of upper chern rank and even cup length of a finite connected CW-complex and prove that upper chern rank is a homotopy invariant. It turns out that determination of upper chern rank of a space sometimes helps to detect whether a generator of the top cohomology group can be realized as Euler class for some real (orientable) vector bundle over or not. For a closed connected -dimensional complex manifold we obtain...
On décrit un exemple de variété de contact universellement tendue qui devient vrillée après une chirurgie de Dehn admissible sur un entrelacs transverse.
We present a direct analytic treatment of the Rokhlin congruence formula R2 by calculating the adiabatic limit of -invariants of Dirac operators on circle bundles. Extensions to higher dimensions are obtained.
Le but de ce travail est double : d’une part, généraliser la construction des classes exotiques pour l’appliquer à d’autres problèmes géométriques que ceux issus des -structures ; d’autre part, préciser, grâce à la notion de -connexité, remplaçant avantageusement les formules de dérivation utilisées précédemment, l’argument d’invariance homotopique permettant d’obtenir des théorèmes de rigidité, montrant simultanément pourquoi la seule connexité des ensembles de connexions considérés ne suffit...
This work is a contribution to study residues of real characteristic classes of vector bundles on which act compact Lie groups. By using the Cech-De Rham complex, the realisation of the usual Thom isomorphism permites us to illustrate localisation techniques of some topological invariants.