Multivariable cochain operations and little 𝑛-cubes

McClure, James; Smith, Jeffrey

doi:10.1090/S0894-0347-03-00419-3

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ISSN 1088-6834(online) ISSN 0894-0347(print)

Multivariable cochain operations and little -cubes

Authors: James E. McClure and Jeffrey H. Smith
Journal: J. Amer. Math. Soc. 16 (2003), 681-704
MSC (2000): Primary 18D50; Secondary 55P48, 16E40
Posted: January 3, 2003
MathSciNet review: 1969208
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Abstract: In this paper we construct a small $E_\infty$ chain operad $\mathcal{S}$ which acts naturally on the normalized cochains of a topological space. We also construct, for each , a suboperad $\mathcal{S}_n$ which is quasi-isomorphic to the normalized singular chains of the little -cubes operad. The case leads to a substantial simplification of our earlier proof of Deligne's Hochschild cohomology conjecture.

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