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

Martin Čadek; Jiří Vanžura

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 4, page 727-736
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Čadek, Martin, and Vanžura, Jiří. "On oriented vector bundles over CW-complexes of dimension 6 and 7." Commentationes Mathematicae Universitatis Carolinae 33.4 (1992): 727-736. <http://eudml.org/doc/247384>.

@article{Čadek1992,
abstract = {Necessary and sufficient conditions for the existence of $n$-dimensional oriented vector bundles ($n=3,4,5$) over CW-complexes of dimension $\le 7$ 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.},
author = {Čadek, Martin, Vanžura, Jiří},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {CW-complex; oriented vector bundle; characteristic classes; Postnikov tower; -dimensional oriented vector bundles over CW-complexes; prescribed Stiefel-Whitney classes; Pontryagin class; span of 6 and 7-dimensional oriented vector bundles},
language = {eng},
number = {4},
pages = {727-736},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On oriented vector bundles over CW-complexes of dimension 6 and 7},
url = {http://eudml.org/doc/247384},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Čadek, Martin
AU - Vanžura, Jiří
TI - On oriented vector bundles over CW-complexes of dimension 6 and 7
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 4
SP - 727
EP - 736
AB - Necessary and sufficient conditions for the existence of $n$-dimensional oriented vector bundles ($n=3,4,5$) over CW-complexes of dimension $\le 7$ 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.
LA - eng
KW - CW-complex; oriented vector bundle; characteristic classes; Postnikov tower; -dimensional oriented vector bundles over CW-complexes; prescribed Stiefel-Whitney classes; Pontryagin class; span of 6 and 7-dimensional oriented vector bundles
UR - http://eudml.org/doc/247384
ER -

References

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  1. Čadek M., Vanžura J., On the classification of oriented vector bundles over 5-complexes, preprint. MR1258434
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  8. Thomas E., Homotopy classification of maps by cohomology homomorphisms, Trans. Amer. Math. Soc. (1964), 111 138-151. (1964) Zbl0119.18401MR0160212
  9. Thomas E., Seminar on fibre bundles, Lecture Notes in Math., no 13 Springer Berlin - Heidelberg - New York (1966). (1966) MR0203733
  10. Thomas E., Postnikov invariants and higher order cohomology operation, Ann. of Math. (1967), 85 184-217. (1967) MR0210135
  11. Thomas E., Real and complex vector fields on manifolds, J. Math. Mech. (1967), 16 1183-1206. (1967) Zbl0153.53503MR0210136
  12. Thomas E., Fields of k -planes on manifolds, Invent. Math. (1967), 3 334-347. (1967) MR0217814
  13. Thomas E., Vector fields on low dimensional manifolds, Math. Z. (1968), 103 85-93. (1968) Zbl0162.55403MR0224109
  14. Woodward L.M., The classification of orientable vector bundles over CW-complexes of small dimension, Proc. Roy. Soc. Edinburgh (1982), 92A 175-179. (1982) Zbl0505.55017MR0677482

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