A proof of the Tsygan formality conjecture for chains.

DOI10.1016/S0001-8708(02)00023-3zbMath1163.53350arXivmath/0010321OpenAlexW2022262693WikidataQ122860591 ScholiaQ122860591MaRDI QIDQ1413189

Boris Shoikhet

Publication date: 16 November 2003

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0010321

Mathematics Subject Classification ID

Related Items (34)

On \(L_\infty\)-morphisms of cyclic chains ⋮ Formality theorems for Hochschild complexes and their applications ⋮ On globalized traces for the Poisson sigma model ⋮ Formal higher-spin theories and Kontsevich-Shoikhet-Tsygan formality ⋮ Characteristic cohomology and observables in higher spin gravity ⋮ Hochschild cohomology of the Weyl algebra and Vasiliev's equations ⋮ Covariant action for conformal higher spin gravity ⋮ Batalin-Vilkovisky algebra structure on Poisson manifolds with diagonalizable modular symmetry ⋮ Compatibility with cap-products in Tsygan's formality and homological Duflo isomorphism ⋮ More on chiral higher spin gravity and convex geometry ⋮ The character map in deformation quantization ⋮ Căldăraru's conjecture and Tsygan's formality ⋮ Calabi-Yau deformations and negative cyclic homology ⋮ Categorical Saito theory. II: Landau-Ginzburg orbifolds ⋮ Higher spin gravities and presymplectic AKSZ models ⋮ The Grothendieck-Teichmüller group action on differential forms and formality morphisms of chains ⋮ Cyclic cohomology of the Weyl algebra ⋮ Multiple zeta values in deformation quantization ⋮ Batalin-Vilkovisky quantization and the algebraic index ⋮ Hochschild cohomology of the Weyl algebra and traces in deformation quantization ⋮ Categorical Saito theory. I: A comparison result ⋮ \(L_\infty \)-resolutions and twisting in the curved context ⋮ Formality theorems for Hochschild chains in the Lie algebroid setting ⋮ The homotopy braces formality morphism ⋮ On the Hochschild homology of elliptic Sklyanin algebras. ⋮ Homology of formal deformations of proper étale Lie groupoids ⋮ Formality and Kontsevich-Duflo type theorems for Lie pairs ⋮ An algebraic index theorem for Poisson manifolds ⋮ Atiyah classes and Kontsevich–Duflo type theorem for dg manifolds ⋮ Poisson cohomology, Koszul duality, and Batalin-Vilkovisky algebras ⋮ \(A_\infty\) algebras from slightly broken higher spin symmetries ⋮ Chiral higher spin gravity in \(\mathrm{(A)dS}_4\) and secrets of Chern-Simons matter theories ⋮ Deformation quantization of the simplest Poisson orbifold ⋮ A formality theorem for Hochschild chains.

Cites Work

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• Hochschild cohomology of the Weyl algebra and traces in deformation quantization
• Tsygan formality and Duflo formula
• Tangent cohomology and cup-product for the Kontsevich quantization
• A path integral approach to the Kontsevich quantization formula.
• The Geometry of the Master Equation and Topological Quantum Field Theory
• Cyclic formality and index theorem
• Vanishing of the Kontsevich integrals of the wheels

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