On Kontsevich's Hochschild cohomology conjecture

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.