This article is cited in 8 papers

$(DA)_\infty$-modules over $(DA)_\infty$-algebras and spectral sequences

S. V. Lapin

Mordovian State University

Abstract: We introduce the construction of a $(DA)_\infty$-(co)module over a $(DA)_\infty$-(co) algebra and study its main homotopy properties. We establish a connection between $(DA)_\infty$-(co)modules over $(DA)_\infty$-(co)algebras and spectral sequences, and thus obtain the structure of an $A_\infty$-comodule over the Milnor $A_\infty$-coalgebra on the homology of any spectrum directly from the differentials of the Adams spectral sequence of this spectrum.

UDC: 513.83

MSC: 55U35, 55T15

Received: 09.04.2001

DOI: 10.4213/im388

 English version: Izvestiya: Mathematics, 2002, 66:3, 543–568

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