SOME NEW FAMILIES OF FILTRATION FOUR IN THE STABLE HOMOTOPY OF SPHERES

This paper proves the existence of 4 families of nontrivial homotopy elements in the stable homotopy of spheres which are represented by α2bn,α2kn, α2gn and α2hnhm in the -terms of the Adams spectral sequence respectively, where α2, bn, kn, gn and hnhm are the known generators in the -terms whose internal degree are 4(p - 1) + 1, 2pn+1(p - 1), (4pn+1 + 2pn) (p - 1),(2pn+1 + 4pn)(p - 1), (2pn + 2pm)(p - 1) respectively and P ≥ 5 is a prime, m ≥ n + 2 ≥ 4.