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 topological model category, we prove a general version of Moss' theorem which applies to spectral sequences that arise from filtrations compatible with the monoidal structure. The theorem has broad applications, e.g. to the computation of the motivic slice and motivic Adams spectral sequences.