Compositions in the v1-periodic homotopy groups of spheres
Martin Bendersky and Donald M. Davis
mbenders@shiva.hunter.cuny.edu, dmd1@lehigh.edu
21 pages, completed March 7, 2000, submitted to Forum Mathematicum
Abstract
Let p_i in pi_{n+8i-1}(S^n) denote an element which suspends to
a generator of the image of the stable 2-primary J-homomorphism.
We determine the image of the composite p_j o p_k in v1-periodic
homotopy v_1^{-1} pi_{n+8i+8j-2}(S^n). The method is to use Adams
operations to compute the 1-line of an unstable homotopy spectral
sequence constructed by Bendersky and Thompson. Odd-primary
analogues are also obtained.