Tamarkin's construction is equivariant with respect to the action of the Grothendieck-Teichmueller group

Abstract

Recall that Tamarkin's construction arXiv:math/9803025, arXiv:math/0003052 gives us a map from the set of Drinfeld associators to the set of homotopy classes of L-infinity quasi-isomorphisms for Hochschild cochains of a polynomial algebra. Due to results of V. Drinfeld (Algebra i Analiz 2, (1990)) and T. Willwacher arXiv:1009.1654 both the source and the target of this map are equipped with natural actions of the Grothendieck-Teichmueller group $GR{T}_1$. In this paper, we use the result from arXiv:1305.4699 to prove that this map from the set of Drinfeld associators to the set of homotopy classes of L-infinity quasi-isomorphisms for Hochschild cochains is $GR{T}_1$-equivariant.

The final version will appear in the Journal of Homotopy and Related Structures

References in corpus (3)

• A tale of three homotopies
• On an enhancement of the category of shifted L-infinity algebras
• Action of derived automorphisms on infinity-morphisms

Cited by in corpus (2)

• On an enhancement of the category of shifted L-infinity algebras
• Action of derived automorphisms on infinity-morphisms