# 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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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 12 December 2015 28 Jan 2016 09:10 05 Apr 2016 19:51 American Mathematical Society 0002-9939 Publisher DOI. An embargo period may apply. https://doi.org/10.1090/proc/12670