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

Martin Čadek; Jiří Vanžura

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 2, page 377-394
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Čadek, Martin, and Vanžura, Jiří. "On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes." Commentationes Mathematicae Universitatis Carolinae 36.2 (1995): 377-394. <http://eudml.org/doc/247775>.

@article{Čadek1995,
abstract = {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.},
author = {Čadek, Martin, Vanžura, Jiří},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {span of the vector bundle; classifying spaces for spinor groups; characteristic classes; Postnikov tower; secondary cohomology operation; span of the vector bundle; classifying spaces for spinor groups; Postnikov tower; characteristic classes; secondary cohomology operation},
language = {eng},
number = {2},
pages = {377-394},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes},
url = {http://eudml.org/doc/247775},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Čadek, Martin
AU - Vanžura, Jiří
TI - On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 2
SP - 377
EP - 394
AB - 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.
LA - eng
KW - span of the vector bundle; classifying spaces for spinor groups; characteristic classes; Postnikov tower; secondary cohomology operation; span of the vector bundle; classifying spaces for spinor groups; Postnikov tower; characteristic classes; secondary cohomology operation
UR - http://eudml.org/doc/247775
ER -

References

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  1. Atiyah M., Dupont J., Vector fields with finite singularities, Acta Math. (1972), 128 1-40. (1972) Zbl0233.57010MR0451256
  2. Borel A., Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. Math. (1953), 57 115-207. (1953) Zbl0052.40001MR0051508
  3. Frank D., On the index of a tangent 2 -field, Topology (1972), 11 245-252. (1972) Zbl0252.57006MR0298689
  4. Hirzebruch F., Neue topologische Methoden in der algebraischen Geometrie, Ergebnisse der Mathematik und ihrer Grenzgebiete, Heft 9, Berlin (1959). (1959) 
  5. Kono A., On the integral cohomology of B S p i n ( n ) , J. Math. Kyoto Univ. (1986), 26:3 333-337. (1986) Zbl0617.55007MR0857221
  6. Massey W.S., On the Stiefel-Whitney classes of a manifold II, Proc. Amer. Math. Soc. (1962), 13 938-942. (1962) Zbl0109.15902MR0142129
  7. Milnor J., Some consequences of a theorem of Bott, Ann. of Math. (1958), 68 444-449. (1958) Zbl0085.17301MR0102805
  8. Mosher R.E., Tangora M.C., Cohomology operations and applications in homotopy theory, Harper & Row, Publishers New York, Evanston and London (1968). (1968) Zbl0153.53302MR0226634
  9. Tze-Beng Ng, On the geometric dimension of the vector bundles, span of a manifold and immersions of manifolds in manifolds, Exposition. Math. (1990), 8 193-226. (1990) MR1062767
  10. Paechter G., The groups π r ( V n , m ) : I, Quart. J. Math., Oxford Ser. (2) (1956), 7 243-268. (1956) MR0131878
  11. Quillen D., The mod 2 cohomology rings of extra-special 2 -groups and the spinor groups, Math. Ann. (1971), 194 197-212. (1971) Zbl0225.55015MR0290401
  12. Thomas E., The index of a tangent 2 -field, Comment. Math. Helvet. (1967), 42 86-110. (1967) Zbl0153.53504MR0215317
  13. Thomas E., Complex structures on real vector bundles, Am. J. Math. (1966), 89 887-908. (1966) MR0220310
  14. Thomas E., On the cohomology of the real Grassmann complexes, Trans. Amer. Math. Soc. (1960), 96 67-89. (1960) Zbl0098.36301MR0121800
  15. Thomas E., On the cohomology groups of the classifying space for the stable spinor group, Bol. Soc. Math. Mex. (1962), 57-69. (1962) Zbl0124.16401MR0153027
  16. Thomas E., Postnikov invariants and higher order cohomology operation, Ann. of Math. (1967), 85 184-217. (1967) MR0210135

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