An application of unstable \(K\)-theory (Q2567326)

The authors continue their work on unstable \(K\)-theory [J. Math. Kyoto Univ. 43, No.~2, 333--348 (2003; Zbl 1070.55007)]. Recall that they defined the unstable \(K\)-theory groups of a CW-complex \(X\) as the set of homotopy classes of maps from \(X\) to the unitary group \(U(n)\). They obtain a result relating such groups and apply it to reprove a result of \textit{S. Oka} [Adv. Stud. Pure Math. 9, 195--230 (1987; Zbl 0638.57018)] regarding an exceptional Lie group.