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Mat. Sb. (N.S.), 1981, Volume 115(157), Number 1(5), Pages 146–158 (Mi msb2379)  

This article is cited in 23 scientific papers (total in 23 papers)

On the cochain complex of topological spaces

V. A. Smirnov


Abstract: Let $X$ be a topological space and $C^*(X; R)$ the cochain complex with coefficients in $R$.
In this paper it is shown that one can define on $C^*(X; R)$ the structure of algebras over an $E_\infty$-operad, and the $B$-construction is carried out. The $B$-construction is an $E_\infty$-algebra that makes it possible to define an $E_\infty$-structure on the cochain complex of loop spaces.
Bibliography: 8 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 43:1, 133–144

Bibliographic databases:

UDC: 513.836
MSC: Primary 55U15; Secondary 55R20, 55T10, 55U25, 18G35
Received: 12.03.1980

Citation: V. A. Smirnov, “On the cochain complex of topological spaces”, Mat. Sb. (N.S.), 115(157):1(5) (1981), 146–158; Math. USSR-Sb., 43:1 (1982), 133–144

Citation in format AMSBIB
\Bibitem{Smi81}
\by V.~A.~Smirnov
\paper On the cochain complex of topological spaces
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 115(157)
\issue 1(5)
\pages 146--158
\mathnet{http://mi.mathnet.ru/msb2379}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=618592}
\zmath{https://zbmath.org/?q=an:0509.55012}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 1
\pages 133--144
\crossref{https://doi.org/10.1070/SM1982v043n01ABEH002437}


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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. V. A. Smirnov, “Homotopy theory of coalgebras”, Math. USSR-Izv., 27:3 (1986), 575–592  mathnet  crossref  mathscinet  zmath
    2. V. A. Khinich, V. V. Schechtman, “The homotopy limit of homotopy algebras”, Russian Math. Surveys, 41:3 (1986), 213–214  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Smirnov V., “Secondary Cohomological Operations”, 288, no. 2, 1986, 301–304  mathscinet  zmath  isi
    4. Hinich V., Schechtman V., “On Homotopy Limit of Homotopy Algebras”, Lect. Notes Math., 1289 (1987), 240–264  crossref  mathscinet  zmath  isi
    5. Smirnov V., “Homology of a-Infinity-Algebras”, Dokl. Akad. Nauk, 330:4 (1993), 441–443  mathnet  mathscinet  zmath  isi
    6. V. A. Smirnov, “Homology of $B$-constructions and co-$B$-constructions”, Russian Acad. Sci. Izv. Math., 45:1 (1995), 79–95  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. S. V. Lapin, “Bordism groups of Poincare $E_\infty$-coalgebras and symmetric $L$-groups”, Sb. Math., 186:7 (1995), 1023–1055  mathnet  crossref  mathscinet  zmath  isi
    8. V. A. Smirnov, “Calculation of the $E_\infty$-structure on the Milnor coalgebra”, Math. Notes, 62:3 (1997), 399–401  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. V. A. Smirnov, “Lie algebras over operads and their applications in homotopy theory”, Izv. Math., 62:3 (1998), 549–580  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. V. A. Smirnov, “The Dyer–Lashof algebra and the Steenrod algebra for generalized homology and cohomology”, Sb. Math., 190:12 (1999), 1807–1842  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. V. A. Smirnov, “A Degeneracy Criterion for $A_\infty$-Structures”, Math. Notes, 69:6 (2001), 827–832  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. S. V. Lapin, “Differential perturbations and $D_\infty$-differential modules”, Sb. Math., 192:11 (2001), 1639–1659  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. V. A. Smirnov, “The $A_\infty$-structures and differentials of the Adams spectral sequence”, Izv. Math., 66:5 (2002), 1057–1086  mathnet  crossref  crossref  mathscinet  zmath
    14. Smirnov V., Sergeraert F., “The Homology of Iterated Loop Spaces”, Forum Math., 14:3 (2002), 345–381  crossref  mathscinet  zmath  isi
    15. S. V. Lapin, “$D_\infty$-differential $E_\infty$-algebras and multiplicative spectral sequences”, Sb. Math., 196:11 (2005), 1627–1658  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. V. A. Smirnov, “Homotopy Theories of Algebras over Operads”, Math. Notes, 78:2 (2005), 251–257  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    17. Smirnov V.A., “Homotopy Theories of Algebras Over Operads”, Homol. Homotopy Appl., 7:2 (2005), 179–187  mathscinet  zmath  isi  elib
    18. S. V. Lapin, “$D_\infty$-differential $E_\infty$-algebras and spectral sequences of $D_\infty$-differential modules”, J. Math. Sci., 159:6 (2009), 819–832  mathnet  crossref  mathscinet  zmath  elib
    19. S. V. Lapin, “$D_\infty$-differential $E_\infty$-algebras and spectral sequences of fibrations”, Sb. Math., 198:10 (2007), 1379–1406  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    20. 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
    21. Smirnov V.A., “Differentials of the Adams spectral sequence and the Kervaire invariant”, Dokl. Math., 80:1 (2009), 573–576  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    22. 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
    23. Michael Ching, “A note on the composition product of symmetric sequences”, J. Homotopy Relat. Struct, 2012  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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