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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb. (N.S.), 1981 Volume 115(157), Number 1(5), Pages 146–158 (Mi sm2379)

This article is cited in 26 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.

UDC: 513.836

MSC: Primary 55U15; Secondary 55R20, 55T10, 55U25, 18G35

Received: 12.03.1980


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

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© Steklov Math. Inst. of RAS, 2025