Obstruction Theory in Fiber Spaces.
Obstructions for Clifford Structures on Vector Bundles.
Obstructions to the section problem in a fibration with a weak formal base.
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 3-Manifolds with Finite Solvable Fundamental Groups.
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 a certain formula for exotic characteristic classes I.
On a generalization of the Conley index
In this note we present the main ideas of the theory of the Conley index over a base space introduced in the papers [7, 8]. The theory arised as an attempt to solve two questions concerning the classical Conley index. In the definition of the index, the exit set of an isolating neighborhood is collapsed to a point. Some information is lost on this collapse. In particular, topological information about how a set sits in the phase space is lost. The first question addressed is how to retain some of...
On affine transformations of Banachable bundles
On Bott-periodic algebraic K-theory.
Let K*(A;Z/ln) denote the mod-ln algebraic K-theory of a Z[1/l]-algebra A. Snaith ([14], [15], [16]) has studied Bott-periodic algebraic theory Ki(A;Z/ln)[1/βn], a localized version of K*(A;Z/ln) obtained by inverting a Bott element βn. For l an odd prime, Snaith has given a description of K*(A;Z/ln)[1/βn] using Adams maps between Moore spectra. These constructions are interesting, in particular for their connections with Lichtenbaum-Quillen conjecture [16].In this paper we obtain a description...
On bundles over a sphere with fibre Euclidean space
On certain homotopy actions of general linear groups on iterated products
The -fold product of an arbitrary space usually supports only the obvious permutation action of the symmetric group . However, if is a -complete, homotopy associative, homotopy commutative -space one can define a homotopy action of on . In various cases, e.g. if multiplication by is null homotopic then we get a homotopy action of for some . After one suspension this allows one to split using idempotents of which can be lifted to . In fact all of this is possible if is an -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 F-connections
On Fibrations and nilpotency - some remarks upon two articles by I. M. James.
On fibrations with the Grassmann manifold of two-planes as fiber.
On finite subgroups of groups of type VF.
On forms and connections on fibre bundles