The diffeomorphism type of certain 𝑆³-bundles over 𝑆⁴

Sanchez, Marc; Wilhelm, Frederick

doi:10.1090/S0002-9939-01-06380-8

The diffeomorphism type of certain $S^{3}$-bundles over $S^{4}$
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by Marc Sanchez and Frederick Wilhelm

Proc. Amer. Math. Soc. 130 (2002), 1139-1143

DOI: https://doi.org/10.1090/S0002-9939-01-06380-8

Published electronically: November 9, 2001

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Abstract:

In this note we show that the unit tangent bundle of $S^{4}$ is diffeomorphic to the total space of a certain principal $S^{3}$-bundle over $S^{4}$, solving a problem of James and Whitehead.

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