The unstable Adams spectral sequence for two-stage towers

✍ Scribed by Kathryn Lesh

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 179 KB
• Volume: 101
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(98)00119-9

✦ Synopsis

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.