An elementary section of a bundle

Rigas, A.

doi:10.1090/S0002-9939-1988-0934896-6

An elementary section of a bundle
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by A. Rigas

Proc. Amer. Math. Soc. 102 (1988), 1099-1100

DOI: https://doi.org/10.1090/S0002-9939-1988-0934896-6

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Abstract:

We use the Cayley algebra and triality to provide an explicit section of a principal ${G_2}$-bundleover ${S^7}$. This section is the basic ingredient for a direct, elementary, proof that ${\pi _6}{G_2} \cong {{\mathbf {Z}}_3},{\pi _6}SU(3) \cong {{\mathbf {Z}}_6}$ and ${\pi _6}{S^3} \cong {{\mathbf {Z}}_{12}}$

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