The Image of J in the EHP Sequence

Abstract

The EHP sequence is based on a result of James [J] who showed that there is H a map H such that S _> Q Sn+- > S2n+1 is a fibration when localized at 2. The map Sn ..> Sn+ is usually labeled E. The boundary homomorphism in the homotopy sequence is usually labeled P. For our purposes it will be most convenient to combine all the EHP sequences into one system. This gives the following filtration of O201:S? = Q(S?):