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Mat. Sb., 2007, Volume 198, Number 10, Pages 3–30 (Mi msb1582)  

This article is cited in 8 scientific papers (total in 8 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.

DOI: https://doi.org/10.4213/sm1582

Full text: PDF file (579 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 515.145.256
MSC: Primary 55P43, 55R20, 55U35; Secondary 18D50, 18G35, 18G55, 55T15, 55U10
Received: 08.06.2006 and 29.06.2007

Citation: S. V. Lapin, “$D_\infty$-differential $E_\infty$-algebras and spectral sequences of fibrations”, Mat. Sb., 198:10 (2007), 3–30; Sb. Math., 198:10 (2007), 1379–1406

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Lapin, “Multiplicative $A_\infty$-structure in terms of spectral sequences of fibrations”, J. Math. Sci., 164:1 (2010), 95–118  mathnet  crossref  mathscinet
    2. S. V. Lapin, “Extension of the Multiplication Operation in $E_\infty$-Algebras to an $A_\infty$-Morphism of $E_\infty$-Algebras and Cartan Objects in the Category of May Algebras”, Math. Notes, 89:5 (2011), 672–688  mathnet  crossref  crossref  mathscinet  isi
    3. Y. Gh. Gouda, “On the cohomology of Banach $A_infty$-module over admissible Banach $A_\infty$-algebra”, Journal of the Egyptian Mathematical Society, 20:2 (2012), 53–56  crossref  mathscinet  zmath
    4. S. V. Lapin, “Homotopy Properties of Differential Lie Modules over Curved Coalgebras and Koszul Duality”, Math. Notes, 94:3 (2013), 335–350  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. S. V. Lapin, “Homotopy Simplicial Faces and the Homology of Realizations of Simplicial Topological Spaces”, Math. Notes, 94:5 (2013), 619–635  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Ya. Gouda, “Homotopy Invariance of Perturbations of $D_\infty$-Differential Modules”, Math. Notes, 96:3 (2014), 353–359  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Lapin S.V., “Homotopy Properties of Differential Modules With Simplicial F-Infinity-Faces and D-Infinity-Differential Modules”, Georgian Math. J., 22:4 (2015), 543–562  crossref  mathscinet  zmath  isi  scopus
    8. Lapin V S., “Dihedral Infinity-Simplicial Modules and Dihedral Homology of Involutive Homotopy Unital a(Infinity)-Algebras”, Georgian Math. J., 26:2 (2019), 257–286  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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