Document Type
Article
Publication Date
6-1-2025
Abstract
Moss’ theorem, which relates Massey products in the -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.
Keywords
Toda bracket, Massey product, spectral sequence, Motivic homotopy theory, slice spectral sequence
Language
English
Publication Title
Peking Mathematical Journal
Rights
© The Author(s) 2025. This is an Open Access work distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Belmont, E., Kong, H.J. A Toda Bracket Convergence Theorem for Multiplicative Spectral Sequences. Peking Math J (2025). https://doi.org/10.1007/s42543-025-00099-x
Manuscript Version
Final Publisher Version