Abstract:
The notion of an E∞E∞-algebra with a filtration is introduced. The connections are established between E∞E∞-algebras with filtrations and the theory of D∞D∞-differential
E∞E∞-algebras over fields. Based on the technique of D∞D∞-differential E∞E∞-algebras, the apparatus of spectral sequences is developed for E∞E∞-algebras with filtrations, and applications of this apparatus to the multiplicative cohomology spectral sequences of fibrations are given.
Bibliography: 21 titles.
\Bibitem{Lap07}
\by S.~V.~Lapin
\paper $D_\infty$-differential $E_\infty$-algebras and spectral sequences of fibrations
\jour Sb. Math.
\yr 2007
\vol 198
\issue 10
\pages 1379--1406
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Linking options:
https://www.mathnet.ru/eng/sm1582
https://doi.org/10.1070/SM2007v198n10ABEH003888
https://www.mathnet.ru/eng/sm/v198/i10/p3
This publication is cited in the following 9 articles:
Lapin V S., “Homotopy Invariance of the Cyclic Homology of a(Infinity)-Algebras Under Homotopy Equivalences of a(Infinity)-Algebras”, Georgian Math. J., 28:6 (2021), 895–916
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
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
Ya. Gouda, “Homotopy Invariance of Perturbations of D∞D∞-Differential Modules”, Math. Notes, 96:3 (2014), 353–359
S. V. Lapin, “Homotopy Properties of Differential Lie Modules over Curved Coalgebras and Koszul Duality”, Math. Notes, 94:3 (2013), 335–350
S. V. Lapin, “Homotopy Simplicial Faces and the Homology of Realizations of Simplicial Topological Spaces”, Math. Notes, 94:5 (2013), 619–635
Y. Gh. Gouda, “On the cohomology of Banach AinftyAinfty-module over admissible Banach A∞A∞-algebra”, Journal of the Egyptian Mathematical Society, 20:2 (2012), 53–56
S. V. Lapin, “Extension of the Multiplication Operation in E∞E∞-Algebras to an A∞A∞-Morphism of E∞E∞-Algebras and Cartan Objects in the Category of May Algebras”, Math. Notes, 89:5 (2011), 672–688
S. V. Lapin, “Multiplicative A∞A∞-structure in terms of spectral sequences of fibrations”, J. Math. Sci., 164:1 (2010), 95–118
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