On the $A_\infty$-Formality conjecture

Abstract: It is proved that the associative differential graded algebra of (polynomial) polyvector fields on a vector space (may be infinite- dimensional) is quasi-isomorphic to the corresponding cohomological Hochschild complex of (polynomial) functions on this vector space as an associative differential graded algebra. This result is an

A_{i} n f t y

-version of the Formality conjecture of Maxim Kontsevich [K].

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