Equivalence of formalities of the little discs operad

Abstract

We show that Kontsevich's formality of the little disk operad, obtained using graphs, is homotopic to Tamarkin's formality, for a special choice of a Drinfeld associator. The associator is given by parallel transport of the Alekseev-Torossian connection.

References in corpus (2)

• Kontsevich deformation quantization and flat connections
• The Kashiwara-Vergne conjecture and Drinfeld's associators

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• Cyclic operad formality for compactified moduli spaces of genus zero surfaces
• Embedding calculus and grope cobordism of knots
• Quadratic Algebras arising from Hopf operads generated by a single element
• Graph Complexes and higher genus Grothendieck-Teichmüller Lie algebras
• The Grothendieck-Teichmüller group action on differential forms and formality morphism of chains
• Formal weights in Kontsevich's formality construction and multiple zeta values
• On rational Drinfeld associators
• On triviality of the Kashiwara-Vergne problem for quadratic Lie algebras