Let an n-algebra mean an algebra over the chain complex of the little n-cubes operad. We give a proof of Kontsevichs conjecture, which states that for a suitable notion of Hochschild cohomology in the category of n-algebras, the Hochschild cohomology complex of an n-algebra is an (n+1)-algebra. This generalizes a conjecture by Deligne for n=1, now proven by several authors.
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