The tangent bundle of an 𝐻-manifold

Kaminker, Jerome

doi:10.1090/S0002-9939-1973-0319187-8

The tangent bundle of an $H$-manifold
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Proc. Amer. Math. Soc. 41 (1973), 305-308 Request permission

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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