On Kontsevich's Hochschild cohomology conjecture
P. Hu, I. Kriz, A. A. Voronov

TL;DR
This paper proves Kontsevich's conjecture that the Hochschild cohomology of an n-algebra naturally forms an (n+1)-algebra, extending Deligne's conjecture to higher dimensions.
Contribution
The paper provides a proof of Kontsevich's conjecture, establishing the algebraic structure of Hochschild cohomology for n-algebras.
Findings
Hochschild cohomology complex of an n-algebra is an (n+1)-algebra
Generalizes Deligne's conjecture to higher n
Confirms the algebraic structure in the category of n-algebras
Abstract
Let an n-algebra mean an algebra over the chain complex of the little n-cubes operad. We give a proof of Kontsevich's conjecture, which states that for a suitable notion of Hochschild cohomology in the category of n-algebras, the Hochschild cohomology complex of an n-algebra is an (n+1)-algebra. This generalizes a conjecture by Deligne for n=1, now proven by several authors.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology
