A solution of Deligne's conjecture

Abstract

Deligne asked in 1993 whether the Hochschild cochain complex of an associative ring has a natural action by the singular chains of the little 2-cubes operad. In this paper we give an affirmative answer to this question. We also show that the topological Hochschild cohomology spectrum of an associative ring spectrum has an action of an operad equivalent to the little 2-cubes.

References in corpus (4)

• Operads and Motives in Deformation Quantization
• Operads, homotopy algebra and iterated integrals for double loop spaces
• Homotopy G-algebras and moduli space operad
• Formality of Chain Operad of Small Squares

Cited by in corpus (12)

• Deformations of algebras over operads and Deligne's conjecture
• The topology of spaces of knots
• Monopole Operators and Bulk-Boundary Relation in Holomorphic Topological Theories
• On Quantum Obstruction Spaces and Higher Codimension Gauge Theories
• Operations on the Hochschild Bicomplex of a Diagram of Algebras
• Secondary products in supersymmetric field theory
• Brace algebras and the cohomology comparison theorem
• What do DG categories form?
• A proof of the contractibility of the 2-operad defined via the twisted tensor product
• Lectures on Symplectic Geometry, Poisson Geometry, Deformation Quantization and Quantum Field Theory
• The Tamarkin--Tsygan calculus of an algebra a la Stasheff
• On the cobar construction of a bialgebra