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The classification of orientable vector bundles over CW-complexes of small dimension

Published online by Cambridge University Press:  14 November 2011

L. M. Woodward
L. M. Woodward
Affiliation:
Department of Mathematics, University of Durham, Durham
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Synopsis

The classification of orientable vector bundles over CW-complexes of dimension ≦8 is given in terms of characteristic classes using elementary homotopy theoretic methods and relations among characteristic classes.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 3-4 , 1982 , pp. 175 - 179
Copyright
Copyright © Royal Society of Edinburgh 1982

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References

1Borel, A. and Serre, J.-P.. Groupes de Lie et puissances réduites de Steenrod. Amer. J. Math. 75 (1953), 409–448.CrossRefGoogle Scholar
2Bott, R. and Milnor, J.. On the parallelizability of the spheres. Bull. Amer. Math. Soc. 64 (1958), 87–89.CrossRefGoogle Scholar
3Dold, A. and Whitney, H.. Classification of oriented sphere bundles over a 4-complex. Ann. of Math. 69 (1959), 667–677.CrossRefGoogle Scholar
4James, I. M. and Thomas, E.. An approach to the enumeration problem for non-stable vector bundles. J. Math. Mech. 14 (1965), 485–506.Google Scholar
5Milnor, J.. Some consequences of a theorem of Bott. Ann. of Math. 68 (1958), 444–449.CrossRefGoogle Scholar
6Pontrjagin, L. S.. Classification of some skew products. Dokl. Acad. Nauk SSSR 47 (1945), 322–325.Google Scholar
7Serre, J.-P.. Cohomologie mod 2 des complexes d'Eilenberg-Maclane. Comment. Math. Helv. 27 (1953), 198–231.CrossRefGoogle Scholar
8Thomas, E.. On the cohomology of the real Grassmann complexes and the characteristic classes of n-plane bundles. Trans. Amer. Math. Soc. 96 (1960), 67–89.Google Scholar
9Thomas, E.. Homotopy classification of maps by cohomology homomorphisms. Trans. Amer. Math. Soc. 111 (1964), 138–151.CrossRefGoogle Scholar
10Whitehead, J. H. C.. On simply connected 4-dimensional polyhedra. Comment Math. Helv. 22 (1949), 48–92.CrossRefGoogle Scholar
11Woodward, L. M.. The classification of principal PUn-bundles over a 4-complex. J. London Math. Soc. (to appear).Google Scholar