The Hopf invariant and homotopy groups of spheres

Abstract

In (5), Whitehead introduced a generalization of the Hopfinvariant in the form of a homomorphism H: πr(Sn) → πr(S2n−1), valid† if r < 3n − 3. In (2), the author extended Whitehead's definition to cover the cases r ≤ 4n − 4; r = 5, n = 2; r = 13, n = 4. He also defined, without restriction, a homomorphismwhich was related to H, whenever H was defined, by the equation H* = FH, F being the Freudenthal suspension