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A Note on Homotopy Invariance of Tangent Bundles

Published online by Cambridge University Press:  22 January 2016

Hiroyasu Ishimoto
Hiroyasu Ishimoto*
Affiliation:
Kanazawa University
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Although tangent bundles of manifolds are not always homotopically invariant, but in some categories of the manifolds they can be homotopically invariant.

In this note, I show that tangent bundles of π-manifolds and almost parallelizable manifolds depend only on their homotopy types.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 31 , January 1968 , pp. 247 - 250
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Bredon, G.E. and Kosinski, A., Vector fields on π-manifolds, Ann. of Math., 84 (1966), 85–90.CrossRefGoogle Scholar
[2] Hsiang, Wu-chung, A note on free differentiable actions of S1 and S3 on homotopy spheres, Ann. of Math., 83 (1966), 266–272.CrossRefGoogle Scholar
[3] Milnor, J., On the immersion of n-manifolds in (n+1)-space, Comment. Math. Helv., 30 (1955), 275–284.CrossRefGoogle Scholar
[4] Milnor, J. and Kervaire, M., Bernoulli numbers, homotopy groups and a theorem of Roholin, Proc. Int. Congress of Math., Edinburgh, 1958.Google Scholar
[5] Kervaire, M. and Milnor, J., Groups of homotopy spheres, I, Ann. of Math., 77 (1963), 504–537.CrossRefGoogle Scholar
[6] Shiraiwa, K., A note on tangent bundles, Nagoya Math. Jour., to appear.Google Scholar
[7] Shiraiwa, K., A note on tangential equivalences., to appear.CrossRefGoogle Scholar
[8] Steenrod, N.E., The topology of fibre bundles, Princeton, 1951.CrossRefGoogle Scholar