Immersionen höherer Ordnung kompakter Mannigfaltigkeiten in euklidische Räume
Independent Rigid Secondary Classes for Holomorphic Foliations.
Index invariants of orbit spaces.
Integrality relations on smooth manifolds.
Invariance par homotopie de la signature à coefficients dans un fibré presque plat.
Invariants from triangulations of hyperbolic 3-manifolds.
Isoparametric Hypersurfaces with Four or Six Distinct Principal Curvatures. Necessary Conditions on the Multiplicities.
Isotropic characteristic classes
K3 surfaces: moduli spaces and Hilbert schemes.
Karoubi’s relative Chern character and Beilinson’s regulator
We construct a variant of Karoubi’s relative Chern character for smooth varieties over and prove a comparison result with Beilinson’s regulator with values in Deligne-Beilinson cohomology. As a corollary we obtain a new proof of Burgos’ Theorem that for number fields Borel’s regulator is twice Beilinson’s regulator.
K-theory, flat bundles and the Borel classes
Using Hausmann and Vogel's homology sphere bundle interpretation of algebraic K-theory, we construct K-theory invariants by a theory of characteristic classes for flat bundles. It is shown that the Borel classes are detected this way, as well as the rational K-theory of integer group rings of finite groups.
K-theory over C*-algebras
The contents of the article represents the minicourse which was delivered at the 7th conference "Geometry and Topology of Manifolds. The Mathematical Legacy of Charles Ehresmann", Będlewo (Poland), 8.05.2005 - 15.05.2005. The article includes the description of the so called Hirzebruch formula in different aspects which lead to a basic list of problems related to noncommutative geometry and topology. In conclusion, two new problems are presented: about almost flat bundles and about the Noether decomposition...
«La classe duale aux points doubles» d'une application
La conjecture des immersions
La géométrie différentielle dans la catégorie
La catégorie des fibrés vectoriels sur les variétés linéaires par morceaux se plonge dans une catégorie des classes d’équivalence de faisceaux de modules sur les faisceaux de germes des fonctions lissables, et on construit les classes de Pontrjagin, vérifiant des axiomes habituels. Chaque variété possède un objet tangent dans cette catégorie, et est la classe totale de Pontrjagin associée à .
Le calcul des classes duales aux singularités de Boardman d'ordre deux
Les inégalités de Morse
Lie theory and the Chern–Weil homomorphism
Line bundles with
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.
Line Fields with Branch Defects.