Hochschild-Kostant-Rosenberg maps twisted by the square root of the Todd class produce an isomorphism of calculi between Tamarkin-Tsygan and Cartan calculi on every dg manifold.
Shifted derived Poisson manifolds associated with Lie pairs
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Duflo--Kontsevich-type isomorphisms for Tamarkin--Tsygan calculi of dg manifolds
Hochschild-Kostant-Rosenberg maps twisted by the square root of the Todd class produce an isomorphism of calculi between Tamarkin-Tsygan and Cartan calculi on every dg manifold.