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On 2-distributions in 8-dimensional vector bundles over 8-complexes

Martin Čadek, Jiří Vanžura (1996)

Colloquium Mathematicae

It is shown that the 2 -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

Martin Čadek, Jiří Vanžura (1998)

Colloquium Mathematicae

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 generalization of the Conley index

Marian Mrozek, James Reineck, Roman Srzednicki (1999)

Banach Center Publications

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 Bott-periodic algebraic K-theory.

Felipe Zaldívar (1994)

Publicacions Matemàtiques

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 certain homotopy actions of general linear groups on iterated products

Ran Levi, Stewart Priddy (2001)

Annales de l’institut Fourier

The n -fold product X n of an arbitrary space usually supports only the obvious permutation action of the symmetric group Σ n . However, if X is a p -complete, homotopy associative, homotopy commutative H -space one can define a homotopy action of GL n ( p ) on X n . In various cases, e.g. if multiplication by p r is null homotopic then we get a homotopy action of G L n ( / p r ) for some r . After one suspension this allows one to split X n using idempotents of 𝔽 p GL n ( / p ) which can be lifted to 𝔽 p GL n ( / p r ) . In fact all of this is possible if X is an H -space...

On contact p -spheres

Mathias Zessin (2005)

Annales de l’institut Fourier

We study invariant contact p -spheres on principal circle-bundles and solve the corresponding existence problem in dimension 3. Moreover, we show that contact p - spheres can only exist on ( 4 n - 1 ) -dimensional manifolds and we construct examples of contact p -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 p -sphere.

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