Tamarkin’s construction is equivariant with respect to the action of the Grothendieck–Teichmueller group

Abstract

© 2015, Tbilisi Centre for Mathematical Sciences. Recall that Tamarkin’s construction (Hinich, Forum Math 15(4):591–614, 2003, arXiv:math.QA/0003052; Tamarkin, 1998, arXiv:math/9803025) gives us a map from the set of Drinfeld associators to the set of homotopy classes of L∞ quasi-isomorphisms for Hochschild cochains of a polynomial algebra. Due to results of Drinfeld (Algebra i Analiz 2(4):149–181, 1990 and Willwacher Invent Math 200(3):671–760, 2015 both the source and the target of this map are equipped with natural actions of the Grothendieck–Teichmueller group GRT1. In this paper, we use the result from Paljug (JHRS, 2015, arXiv:1305.4699) to prove that this map from the set of Drinfeld associators to the set of homotopy classes of L∞ quasi-isomorphisms for Hochschild cochains is GRT1-equivariant.