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.References
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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
- MR Author ID: 823360
- Email: thomas.willwacher@math.uzh.ch
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 5181-5193
- MSC (2010): Primary 18D50
- DOI: https://doi.org/10.1090/proc/12670
- MathSciNet review: 3411136