  We prove a conjecture of Kontsevich which states that if $A$ is an $E_{d-1}$
algebra then the Hochschild cohomology object of $A$ is the universal $E_d$
algebra acting on $A$. The notion of an $E_d$ algebra acting on an $E_{d-1}$
algebra was defined by Kontsevich using the swiss cheese operad of Voronov. The
degree 0 and 1 pieces of the swiss cheese operad can be used to build a
cofibrant model for $A$ as an $E_{d-1}-A$ module. The theorem amounts to the
fact that the swiss cheese operad is generated up to homotopy by its degree 0
and 1 pieces.
