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Is there a refinement of the Hochschild-Kostant-Rosenberg theorem for cohomology?

Yes there is. It was noted by Kontsevich long time ago that the HKR quasi-isomorphism on cochains can be corrected to give a quasi-isomorphism of dg-algebras and thus induce an $A_\infty$ quasi-isomo …
Tony Pantev's user avatar
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