Journal of the American Mathematical Society

Author(s): James E. McClure; Jeffrey H. Smith
Journal: J. Amer. Math. Soc. 16 (2003), 681-704.
MSC (2000): Primary 18D50; Secondary 55P48, 16E40
Posted: January 3, 2003
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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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James E. McClure
Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907-2067
Email: mcclure@math.purdue.edu

Jeffrey H. Smith
Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907-2067
Email: jhs@math.purdue.edu

DOI: 10.1090/S0894-0347-03-00419-3
PII: S 0894-0347(03)00419-3
Received by editor(s): June 25, 2001
Received by editor(s) in revised form: June 28, 2002.
Posted: January 3, 2003
Additional Notes: The first author was partially supported by NSF grant DMS-9971953. He thanks the Lord for making his work possible
The second author was partially supported by NSF grant DMS-9971953
Copyright of article: Copyright 2003, American Mathematical Society

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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