EHP sequences in BP theory

Abstract

We have given the homomorphisms in these sequences their usual names: E for suspension, H for Hopf invariant, and P for Whitehead product. When the prime p = 2, it also happens that 9’” = S2n, and the EHP sequences provide a way of calculating the groups TV, inductive on the sphere dimension n, and on the stem dimension q-n. When p is an odd prime, the space 3’” (which has cells in each dimension 2n, 4n,. . ., 2n(p 1)) replaces the even dimensional sphere in the EHP induction. The homotopy groups of the even-dimensional spheres localized at p may be obtained from the fibration