We prove a conjecture of Kontsevich (Kon99) which states that if A is an Ed-1 algebra then the Hochschild cohomology object of A is the universal Ed algebra acting on A. The notion of an Ed algebra acting on an Ed -1 operad was also defined by Kontsevich using the swiss cheese operad of Voronov (Vor99). We prove a homotopical property of the swiss cheese operad from which the conjecture follows.
