Title: The Unstable Adams Spectral Sequence for Two-Stage Towers
Author: Kathryn Lesh
AMS Classification: 55T15, 55Q52, 55R45
Address: Department of Mathematics
University of Toledo
Toledo, OH 43606
E-mail: klesh@uoft02.utoledo.edu
Let KP denote a generalized mod 2 Eilenberg-MacLane space and let Y be
the fiber of a map X -> KP to which the Massey-Peterson theorem
applies. We study the relationship of the mod 2 unstable Adams
spectral sequence (UASS) for X and for Y. Given conditions on X, we
split the E_{2}-term for Y, and we use a primary level calculation to
compute d_{2} for Y up to an error term. If the UASS for X collapses
at E_{2} (for example, if X is an Eilenberg-MacLane space), the UASS
for Y collapses at E_{3}, and we have the entire UASS for Y. We also
give examples and address a conjecture of Bousfield on the UASS for
the Lie group SO.
To appear in: Topology and Its Applications