Kontsevich's Swiss Cheese Conjecture

Abstract

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.

21 pages, 2 figures

References in corpus (6)

• Manin products, Koszul duality, Loday algebras and Deligne conjecture
• Operads revisited
• The homology of the little disks operad
• The A-infinity operad and the moduli space of curves
• Proof of Swiss Cheese Version of Deligne's Conjecture
• Forests and the W Construction

Cited by in corpus (8)

• Derived coisotropic structures I: affine case
• Structured singular manifolds and factorization homology
• Higher Hochschild cohomology of the Lubin-Tate ring spectrum
• Factorization Algebras for Bulk-Boundary Systems
• On Quantum Obstruction Spaces and Higher Codimension Gauge Theories
• Differential calculus of Hochschild pairs for infinity-categories
• Weyl n-algebras and the Swiss cheese operad
• Lax Functors, Cospans, and the Center Construction