This article is cited in 9 papers

$D_\infty$-differential $E_\infty$-algebras and spectral sequences of fibrations

S. V. Lapin

Mordovian State University

Abstract: The notion of an $E_\infty$-algebra with a filtration is introduced. The connections are established between $E_\infty$-algebras with filtrations and the theory of $D_\infty$-differential $E_\infty$-algebras over fields. Based on the technique of $D_\infty$-differential $E_\infty$-algebras, the apparatus of spectral sequences is developed for $E_\infty$-algebras with filtrations, and applications of this apparatus to the multiplicative cohomology spectral sequences of fibrations are given.
Bibliography: 21 titles.

UDC: 515.145.256

MSC: Primary 55P43, 55R20, 55U35; Secondary 18D50, 18G35, 18G55, 55T15, 55U10

Received: 08.06.2006 and 29.06.2007

DOI: 10.4213/sm1582

 English version: Sbornik: Mathematics, 2007, 198:10, 1379–1406

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