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Triviality of the higher formality theorem


Calaque, Damien; Willwacher, Thomas (2015). Triviality of the higher formality theorem. Proceedings of the American Mathematical Society, 143(12):5181-5193.

Abstract

It is noted that the higher version of M. Kontsevich’s Formality Theorem is much easier than the original one. Namely, we prove that the higher Hochschild-Kostant-Rosenberg map taking values in the n-Hochschild complex already respects the natural E$_{n+1}$ operad action whenever n $\ge,$ 2. To this end we introduce a higher version of the braces operad, which—analogously to the usual braces operad—acts naturally on the higher Hochschild complex, and which is a model of the E$_{n+1}$operad.

Abstract

It is noted that the higher version of M. Kontsevich’s Formality Theorem is much easier than the original one. Namely, we prove that the higher Hochschild-Kostant-Rosenberg map taking values in the n-Hochschild complex already respects the natural E$_{n+1}$ operad action whenever n $\ge,$ 2. To this end we introduce a higher version of the braces operad, which—analogously to the usual braces operad—acts naturally on the higher Hochschild complex, and which is a model of the E$_{n+1}$operad.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:12 December 2015
Deposited On:28 Jan 2016 09:10
Last Modified:05 Apr 2016 19:51
Publisher:American Mathematical Society
ISSN:0002-9939
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1090/proc/12670

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