A Decomposability Criterion for Algebraic 2-Bundles on Projective Spaces.
A Definition of Exotic Characteristic Classes of Spherical Fibrations
A remark on the Chern class of a tensor product.
A Remark on Universal Connections.
A splitting principle for group representations.
A universal space for normal bundles of n-manifolds.
Algebraic characteristic classes for idempotent matrices.
This paper contains the algebraic analog for idempotent matrices of the Chern-Weil theory of characteristic classes. This is used to show, algebraically, that the canonical line bundle on the complex projective space is not stably trivial. Also a theorem is proved saying that for any smooth manifold there is a canonical epimorphism from the even dimensional algebraic de Rham cohomology of its algebra of smooth functions onto the standard even dimensional de Rham cohomology of the manifold.
Algebroid nature of the characteristic classes of flat bundles
The following two homotopic notions are important in many domains of differential geometry: - homotopic homomorphisms between principal bundles (and between other objects), - homotopic subbundles. They play a role, for example, in many fundamental problems of characteristic classes. It turns out that both these notions can be - in a natural way - expressed in the language of Lie algebroids. Moreover, the characteristic homomorphisms of principal bundles (the Chern-Weil homomorphism [K4], or the...