# Deformation Quantization of Poisson Manifolds

@article{Kontsevich1997DeformationQO, title={Deformation Quantization of Poisson Manifolds}, author={Maxim Kontsevich}, journal={Letters in Mathematical Physics}, year={1997}, volume={66}, pages={157-216} }

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the algebra of functions on X is in one-to-one correspondence with the set of equivalence classes of Poisson structures on X modulo diffeomorphisms. In fact, a more general statement is proven (the ‘Formality conjecture’), relating the Lie superalgebra of polyvector fields on X and the Hochschild complex…

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