Compositions in the v1-periodic homotopy groups of spheres

This paper, by Martin Bendersky and Donald M. Davis, appeared in Forum Mathematicum 15 (2003) 37-56.. dvi file and ps file


Let p_i in pi_{n+8i-1}(S^n) denote an element which suspends to a generator of the image of the stable J-homomorphism. We determine the image of the composite p_j o p_k in v1-periodic homotopy v1^{-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.