Abstract
Let KP denote a generalized mod 2 EilenbergâMacLane space and let Y be the fiber of a map Xâ KP to which the MasseyâPeterson 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 EilenbergâMacLane 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.
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