%0 Journal Article
%T Kontsevich's Swiss Cheese Conjecture
%A Justin D. Thomas
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1011.1635v3