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.
|Commitee:||Goerss, Paul, Tamarkin, Dmitry|
|School Location:||United States -- Illinois|
|Source:||DAI-B 71/05, Dissertation Abstracts International|
|Keywords:||E_d, E_n, Hochschild cohomology, Kontsevich's conjecture, Swiss cheese operad|
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