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Triviality of the higher formality theorem


Authors: Damien Calaque and Thomas Willwacher
Journal: Proc. Amer. Math. Soc. 143 (2015), 5181-5193
MSC (2010): Primary 18D50
DOI: https://doi.org/10.1090/proc/12670
Published electronically: April 14, 2015
MathSciNet review: 3411136
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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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Additional Information

Damien Calaque
Affiliation: I3M, Université Montpellier 2, Case courrier 051, 34095 Montpellier cedex 5, France
Email: damien.calaque@univ-montp2.fr

Thomas Willwacher
Affiliation: Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
Email: thomas.willwacher@math.uzh.ch

DOI: https://doi.org/10.1090/proc/12670
Received by editor(s): November 23, 2013
Received by editor(s) in revised form: May 5, 2014, and October 31, 2014
Published electronically: April 14, 2015
Additional Notes: The first author acknowledges the support of the Swiss National Science Foundation (grant 200021_137778)
The second author acknowledges the support of the Swiss National Science Foundation (grants PDAMP2_137151 and 200021_150012)
Communicated by: Lev Borisov
Article copyright: © Copyright 2015 American Mathematical Society

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