A solution of Deligne's conjecture

TL;DR

This paper proves that the Hochschild cochain complex of an associative ring admits a natural action by the little 2-cubes operad, confirming Deligne's conjecture from 1993.

Contribution

It provides a positive solution to Deligne's conjecture, establishing a natural operad action on Hochschild cochains and spectra.

Findings

Hochschild cochain complex admits a little 2-cubes operad action

Topological Hochschild cohomology spectrum has an operad action

Confirms Deligne's conjecture from 1993

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.