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A Toda Bracket Convergence Theorem for Multiplicative Spectral Sequences
Abstract Moss’ theorem, which relates Massey products in the$$E_r$$ -page of the classical Adams spectral sequence to Toda brackets of homotopy groups, is one of the main tools for calculating Adams differentials. Working in an arbitrary symmetric monoidal stable simplicial model category, we prove a general version of Moss’ theorem which applies to spectral sequences that arise from filtrations compatible with the monoidal structure. This involves the study of Massey products and Toda brackets in a non-strictly associative context. The theorem has broad applications, e.g., to the computation of the motivic slice spectral sequence and other colocalization towers.
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- Award ID(s):
- 2427220
- PAR ID:
- 10595800
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Peking Mathematical Journal
- ISSN:
- 2096-6075
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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