On 4-fields and 4-distributions in 8-dimensional vector bundles over 8-complexes

Martin Čadek; Jiří Vanžura

Colloquium Mathematicae (1998)

  • Volume: 76, Issue: 2, page 213-228
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Čadek, Martin, and Vanžura, Jiří. "On 4-fields and 4-distributions in 8-dimensional vector bundles over 8-complexes." Colloquium Mathematicae 76.2 (1998): 213-228. <http://eudml.org/doc/210561>.

@article{Čadek1998,
abstract = {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.},
author = {Čadek, Martin, Vanžura, Jiří},
journal = {Colloquium Mathematicae},
keywords = {classifying spaces for groups; vector bundle; higher order cohomology operations; characteristic classes; Postnikov tower; distribution},
language = {eng},
number = {2},
pages = {213-228},
title = {On 4-fields and 4-distributions in 8-dimensional vector bundles over 8-complexes},
url = {http://eudml.org/doc/210561},
volume = {76},
year = {1998},
}

TY - JOUR
AU - Čadek, Martin
AU - Vanžura, Jiří
TI - On 4-fields and 4-distributions in 8-dimensional vector bundles over 8-complexes
JO - Colloquium Mathematicae
PY - 1998
VL - 76
IS - 2
SP - 213
EP - 228
AB - 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.
LA - eng
KW - classifying spaces for groups; vector bundle; higher order cohomology operations; characteristic classes; Postnikov tower; distribution
UR - http://eudml.org/doc/210561
ER -

References

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