Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 18D50

Retrieve articles in all journals with MSC (2010): 18D50


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