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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Multivariable cochain operations and little $n$-cubes
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by James E. McClure and Jeffrey H. Smith PDF
J. Amer. Math. Soc. 16 (2003), 681-704 Request permission

Abstract:

In this paper we construct a small $E_\infty$ chain operad $\mathcal {S}$ which acts naturally on the normalized cochains $S^*X$ of a topological space. We also construct, for each $n$, a suboperad $\mathcal {S}_n$ which is quasi-isomorphic to the normalized singular chains of the little $n$-cubes operad. The case $n=2$ leads to a substantial simplification of our earlier proof of Deligne’s Hochschild cohomology conjecture.
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Additional Information
  • 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
  • Received by editor(s): June 25, 2001
  • Received by editor(s) in revised form: June 28, 2002
  • Published electronically: 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 2003 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 16 (2003), 681-704
  • MSC (2000): Primary 18D50; Secondary 55P48, 16E40
  • DOI: https://doi.org/10.1090/S0894-0347-03-00419-3
  • MathSciNet review: 1969208