A new type of Hopf invariant is described for the fiber of the pinch map:
F → X ∪CA →π SA
and this is used to study the boundary map in the fibration sequence
of Cohen, Moore and Neisendorfer:
Ω2S2n+1
→∂n
ΩFn → ΩP2n+1 →
ΩS2n+1.
The boundary map is shown to be compatible with the Hopf invariant and a filtration of the spliting is obtained.