Triviality of the higher formality theorem

Calaque, Damien; Willwacher, Thomas

doi:10.1090/proc/12670

Triviality of the higher formality theorem
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by Damien Calaque and Thomas Willwacher PDF

Proc. Amer. Math. Soc. 143 (2015), 5181-5193 Request permission

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 $n\geq 2$. 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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