### 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
#### 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 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.