The Hochschild cohomology of a (differential graded associative) algebra is a Gerstenhaber algebra, described by the homology of the little squares operad that characterizes double loop spaces. Deligne conjectured that the Hochschild complex should then be an algebra for an appropriate chain operad that is weakly equivalent to the little squares operad. There are numerous solutions to Deligne's conjecture, from McClure-Smith, Berger-Fresse, and others.

We take another approach to the problem: adapting recent work by Dwyer and Hess, we show that the Hochschild complex is equivalent to something that can be delooped twice; this ``something'' is then naturally an algebra for the little squares operad itself.

This is joint work with Kathryn Hess.