Hopf invariants of the Berstein-Hilton-Ganea kind

We study Hopf invariants of a kind constructed classically by Berstein, Hilton and Ganea. Beyond basic properties of such Hopf invariants we also consider comparisons to other generalizations of the Hopf invariant as have been made by Nomura (1966), Walker (1979) and recently Marcum. Our principal example here of a Hopf invariant of the Berstein-Hilton-Ganea kind is the Ganea-Hopf invariant GHI: ΣΩM(f,g) → ΩCf ∗ ΩCg. The main result we establish for GHI is a computational formula, one term of which involves the dual product of Arkowitz.