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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The tangent bundle of an $ H$-manifold


Author: Jerome Kaminker
Journal: Proc. Amer. Math. Soc. 41 (1973), 305-308
MSC: Primary 55D45; Secondary 55F15
MathSciNet review: 0319187
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Abstract: By an $ H$-manifold we mean a closed, smooth $ ({C^\infty })$ manifold which is an $ H$-space. It is proved that the tangent sphere bundle of an $ H$-manifold is fiber homotopy equivalent to the trivial bundle. This improves a result of W. Browder and E. Spanier which proved only the stable fiber homotopy triviality. As an application, we observe that a $ 1$-connected, finite, CW complex, which is an $ H$-space (and, hence, an $ n$-dimensional Poincaré complex, for some $ n$) is of the homotopy type of a parallelizable manifold, if $ n \ne 4k + 2$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0319187-8
PII: S 0002-9939(1973)0319187-8
Keywords: $ H$-space, fiber homotopy type, tangent sphere bundle, parallelizable manifold
Article copyright: © Copyright 1973 American Mathematical Society