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Torsion Elements and the Classification of Vector Bundles

Published online by Cambridge University Press:  20 November 2018

Robert D. Little*
Affiliation:
University of Hawaii at Manoa, Honolulu, Hawaii
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There are many situations in algebraic topology when a geometric construction is possible if, and only if, a certain integral cohomology class, an obstruction is zero. When attempts are made to compute the obstruction, it often happens that it is relatively easy to show that m times the obstruction is zero, where m is an integer, and consequently the geometric construction is possible if the cohomology group in question has no elements of order m.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Hirsch, M., Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959), 242276.Google Scholar
2. Husemoller, D., Fibre bundles (McGraw Hill, 1966).Google Scholar
3. Jones, I. M. and Thomas, E., An approach to the enumeration problem … , Journ. Math, and Mech. U(1965), 485506.Google Scholar
4. Little, R. D., A relation between obstructions and functional cohomology operations, Proc. Amer. Math. Soc. 49 (1975), 475480.Google Scholar
5. Massey, W. S., On the Stiefel-Whitney classes of a manifold, Amer. J. Math. 82 (1960), 92102.Google Scholar
6. Mosher, R. E. and Tangora, M. C., Cohomology operations and applications in homotopy theory (Harper and Row, 1968).Google Scholar
7. Olum, P., Invariants for effective homotopy classification and extension of mappings, Mem. Amer. Math. Soc. 37 (1961).Google Scholar
8. Olum, P. Factorizations and induced homomorphisms, Adv. in Math. 3 (1969), 72100.Google Scholar
9. Olum, P. Seminar in obstruction theory, Cornell Univ., 1968.Google Scholar
10. Sternstein, M., Necessary and sufficient conditions for homotopy classification by cohomology and homotopy homomorphisms, Proc. Amer. Math. Soc. 34 (1972), 250256.Google Scholar
11. Thomas, E., Homotopy classification by cohomology homomorphisms, Trans. Amer. Math. Soc. 96 (1960), 6789.Google Scholar
12. Thomas, E. Submersions and immersions with codimension one or two, Proc. Amer. Math. Soc. 19 (1968), 859863.Google Scholar
13. Thomas, E. Vector fields on low dimensional manifolds, Math. Zeitschr. 108 (1968), 8593.Google Scholar
14. Thomas, E. Real and complex vector fields on manifolds, Journ. Math, and Mech. 16 (1967), 11831206.Google Scholar