Obstructions for Clifford Structures on Vector Bundles.
On 2-distributions in 8-dimensional vector bundles over 8-complexes
It is shown that the -index of a 2-distribution in an 8-dimensional spin vector bundle over an 8-complex is independent of the 2-distribution. Necessary and sufficient conditions for the existence of 2-distributions in such vector bundles are given in terms of characteristic classes and a certain secondary cohomology operation. In some cases this operation is computed.
On 4-fields and 4-distributions in 8-dimensional vector bundles over 8-complexes
Let ξ be an oriented 8-dimensional spin vector bundle over an 8-complex. In this paper we give necessary and sufficient conditions for ξ to have 4 linearly independent sections or to be a sum of two 4-dimensional spin vector bundles, in terms of characteristic classes and higher order cohomology operations. On closed connected spin smooth 8-manifolds these operations can be computed.
On affine transformations of Banachable bundles
On bundles over a sphere with fibre Euclidean space
On complex structures in 8-dimensional vector bundles.
On complex vector bundles on projective threefolds.
On contact -spheres
We study invariant contact -spheres on principal circle-bundles and solve the corresponding existence problem in dimension 3. Moreover, we show that contact - spheres can only exist on -dimensional manifolds and we construct examples of contact -spheres on such manifolds. We also consider relations between tautness and roundness, a regularity property concerning the Reeb vector fields of the contact forms in a contact -sphere.
On fuzzy subbundles of vector bundles.
On graded algebra bundles.
On higher order point singularities of some geometric object fields
On oriented vector bundles over CW-complexes of dimension 6 and 7
Necessary and sufficient conditions for the existence of -dimensional oriented vector bundles () over CW-complexes of dimension with prescribed Stiefel-Whitney classes , and Pontrjagin class are found. As a consequence some results on the span of 6 and 7-dimensional oriented vector bundles are given in terms of characteristic classes.
On quantizing A-bundles over Hamilton G-spaces
On residue formulas for characteristic numbers
We show that coefficients of residue formulas for characteristic numbers associated to a smooth toral action on a manifold can be taken in a quotient field This yields canonical identities over the integers and, reducing modulo two, residue formulas for Stiefel Whitney numbers.
On the Atiyah-Hitchin-Drinfeld-Manin Vanishing Theorem for Cohomology Groups of Instanton Bundles.
On the classification of oriented vector bundles over 5-complexes
On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes
Necessary and sufficient conditions for the existence of two linearly independent sections in an 8-dimensional spin vector bundle over a CW-complex of the same dimension are given in terms of characteristic classes and a certain secondary cohomology operation. In some cases this operation is computed.
On the fundamental group of a space of sections.