The Homotopy Braces Formality Morphism

Abstract

We extend M. Kontsevich's formality morphism to a homotopy braces morphism and to a homotopy Gerstenhaber morphism. We show that this morphism is homotopic to D. Tamarkin's formality morphism, obtained using formality of the little disks operad, if in the latter construction one uses the Alekseev-Torossian associator. Similar statements can also be shown in the "chains" case, i.e., on Hochschild homology instead of cohomology. This settles two well known and long standing problems in deformation quantization and unifies the several known graphical constructions of formality morphisms and homotopies by Kontsevich, Shoikhet, Calaque, Rossi, Alm, Cattaneo, Felder and the author.

The title was changed in the publication process. The old title was "A Note on Br-infinity and KS-infinity formality". The article will appear under the current title in the Duke Math. Journal

References in corpus (4)

• Hydrodynamic Limit For An Active Exclusion Process
• Formality of the homotopy calculus algebra of Hochschild (co)chains
• Two-colored noncommutative Gerstenhaber formality and infinity Duflo isomorphism
• Tamarkin's construction is equivariant with respect to the action of the Grothendieck-Teichmueller group

Cited by in corpus (14)

• Hydrodynamic Limit For An Active Exclusion Process
• Multiple zeta values in deformation quantization
• Formality and Kontsevich--Duflo type theorems for Lie pairs
• The Lambrechts-Stanley Model of Configuration Spaces
• Quantisation of derived Poisson structures
• Grothendieck-Teichmueller group, operads and graph complexes: a survey
• Polyvector fields and polydifferential operators associated with Lie pairs
• Configuration Spaces of Surfaces
• Formality of a higher-codimensional Swiss-Cheese operad
• A Geometric Approach to Hochschild Cohomology of the Exterior Algebra
• A moperadic approach to cyclotomic associators
• Models for the n-Swiss Cheese operads
• Non-formality of Voronov's Swiss-Cheese operads
• Homotopy Prefactorization Algebras