Kontsevich's Swiss Cheese Conjecture

Details Kontsevich's Swiss Cheese Conjecture Kontsevich's Swiss Cheese Conjecture

2010-11-07

arxiv.org/abs/1011.1635v1

Mathematics

Algebraic Topology

33 pages, 9 figures, rewrite of Northwestern University Ph.D. thesis

Scientific paper

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. We prove a homotopical property of the swiss cheese operad from which the conjecture follows.

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