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

Commentationes Mathematicae Universitatis Carolinae (1992)

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

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topČadek, 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

top- Čadek M., Vanžura J., On the classification of oriented vector bundles over 5-complexes, preprint. MR1258434
- Dold A., Whitney H., Classification of oriented sphere bundles over a 4-complex, Ann. of Math. (1959), 69 667-677. (1959) Zbl0124.38103MR0123331
- James I., Thomas E., An approach to the enumeration problem for non-stable vector bundles, J. Math. Mech. (1965), 14 485-506. (1965) Zbl0142.40701MR0175134
- Milnor J., Some consequences of a theorem of Bott, Ann. of Math. (1958), 68 444-449. (1958) Zbl0085.17301MR0102805
- Tze-Beng Ng, On the geometric dimension of vector bundles, span of manifold and immersion of manifolds in manifolds, Exposition. Math. (1990), 8 193-226. (1990) MR1062767
- Quillen D., The mod 2 cohomology rings of extra-special 2-groups and their spinor groups, Math. Ann. (1971), 194 197-212. (1971) MR0290401
- Thomas E., On the cohomology of the real Grassmann complexes, Trans. Amer. Math. Soc. (1960), 96 67-89. (1960) Zbl0098.36301MR0121800
- Thomas E., Homotopy classification of maps by cohomology homomorphisms, Trans. Amer. Math. Soc. (1964), 111 138-151. (1964) Zbl0119.18401MR0160212
- Thomas E., Seminar on fibre bundles, Lecture Notes in Math., no 13 Springer Berlin - Heidelberg - New York (1966). (1966) MR0203733
- Thomas E., Postnikov invariants and higher order cohomology operation, Ann. of Math. (1967), 85 184-217. (1967) MR0210135
- Thomas E., Real and complex vector fields on manifolds, J. Math. Mech. (1967), 16 1183-1206. (1967) Zbl0153.53503MR0210136
- Thomas E., Fields of $k$-planes on manifolds, Invent. Math. (1967), 3 334-347. (1967) MR0217814
- Thomas E., Vector fields on low dimensional manifolds, Math. Z. (1968), 103 85-93. (1968) Zbl0162.55403MR0224109
- 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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