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arXiv · 1811.03613

The Transition Function of $G_2$ over $S^6$

Ádám Gyenge
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Abstract

We obtain explicit formulas for the trivialization functions of the ${\rm SU}(3)$ principal bundle $G_2 \to S^6$ over two affine charts. We also calculate the explicit transition function of this fibration over the equator of the six-sphere. In this way we obtain a new proof of the known fact that this fibration corresponds to a generator of $\pi_{5}({\rm SU}(3))$.

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Ádám Gyenge. 2018-11-08. The Transition Function of $G_2$ over $S^6$. https://doi.org/10.3842/sigma.2019.078

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