A stable approach to an unstable homotopy spectral sequence
Martin Bendersky
Hunter College, CUNY, NY 10021
mbenders@shiva.hunter.cuny.edu
Donald M. Davis
Lehigh University, Bethlehem, PA 18015
dmd1@lehigh.edu
AMS classification: 55T15, 55Q52
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
2-primary v1-periodic homotopy groups of F4. Some new general results
about convergence of this spectral sequence are also proved.