### A stable approach to an unstable homotopy spectral sequence

This paper, coauthored with Martin Bendersky, appeared in Topology
42 (2003) 1261-1287.
See the dvi file or ps
file.
Abstract: Recently, Bendersky and Thompson introduced a spectral
sequence which, for many spaces X, converges to the v1-periodic
homotopy groups of X. It is proved that the E2-term of this spectral
sequence is given by Ext in the category of stable p-adic Adams modules
of PK^1(X;Zphat)/im(psi^p). We compute this spectral sequence when
p=2 and X is the exceptional Lie group F4, yielding as a new result
the v1-periodic homotopy groups of F4. Some new general results about
convergence of this spectral sequence are also proved.