The Transition Function of G₂ over S⁶

Abstract

We obtain explicit formulas for the trivialization functions of the SU(3) principal bundle G₂→S⁶ 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 π₅(SU(3)).