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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 ℤ 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 analytic torsion over C*-algebras

Alan Carey, Varghese Mathai, Alexander Mishchenko (1999)

Banach Center Publications

In this paper, we present an analytic definition for the relative torsion for flat C*-algebra bundles over a compact manifold. The advantage of such a relative torsion is that it is defined without any hypotheses on the flat C*-algebra bundle. In the case where the flat C*-algebra bundle is of determinant class, we relate it easily to the L^2 torsion as defined in [7],[5].

On oriented vector bundles over CW-complexes of dimension 6 and 7

Martin Čadek, Jiří Vanžura (1992)

Commentationes Mathematicae Universitatis Carolinae

Necessary and sufficient conditions for the existence of n -dimensional oriented vector bundles ( n = 3 , 4 , 5 ) over CW-complexes of dimension ≤ 7 with prescribed Stiefel-Whitney classes w 2 = 0 , w 4 and Pontrjagin class p 1 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 Sp(2) and Sp(2) · Sp(1) structures in 8-dimensional vector bundles.

Martin Cadek, Jirí Vanzura (1997)

Publicacions Matemàtiques

Let ξ be an oriented 8-dimensional vector bundle. We prove that the structure group SO(8) of ξ can be reduced to Sp(2) or Sp(2) · Sp(1) if and only if the vector bundle associated to ξ via a certain outer automorphism of the group Spin(8) has 3 linearly independent sections or contains a 3-dimensional subbundle. Necessary and sufficient conditions for the existence of an Sp(2)- structure in ξ over a closed connected spin manifold of dimension 8 are also given in terms of characteristic classes.

On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes

Martin Čadek, Jiří Vanžura (1995)

Commentationes Mathematicae Universitatis Carolinae

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 topological invariants of vector bundles

Zbigniew Szafraniec (1992)

Annales Polonici Mathematici

Let E → W be an oriented vector bundle, and let X(E) denote the Euler number of E. The paper shows how to calculate X(E) in terms of equations which describe E and W.

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