A note on the Hopf homomorphism of a Toda bracket and its application (Q1890214)

This paper defines a generalized Hopf homomorphism \(H : [\Sigma K, \Sigma A] \rightarrow [\Sigma K, \Sigma(A \wedge A)]\) for a CW-complex \(A\) with a single vertex. The authors relate this homomorphism to the Toda bracket. By applying their results to suspensions of the real projective plane and the quasi-quaternionic projective plane they determine, in a roundabout way, the \(2\)-primary component \(\pi_{14}^{7}\) of the homotopy group \(\pi_{14}(S^{7})\). They also give a short proof of the existence of the unstable Adam's map.