| Abstract: | Abstract Homotopy operations Θ: ΣY, U] → ΣY, V] which are natural in Y are considered. In particular a technique used in the definition of the Hopf invariant (as treated by Berstein-Hilton) shows that any fibration p: E → B with fiber V, when provided with a homotopy section of Ωp, determines such a homotopy operation ΣY, E] → ΣY, V]. More generally, starting from a track class of homotopies α º f ? β º g we adapt this fibration technique to construct a homotopy operation ΣY, M(f,g)] → ΣY, F α * F β] called a Hopf invariant. The intervening fibration in the definition of this Hopf invariant arises via the fiberwise join construction. |
