Brace algebras and the cohomology comparison theorem
arXiv:math/0112177
Abstract
The Gerstenhaber and Schack cohomology comparison theorem asserts that there is a cochain equivalence between the Hochschild complex of a certain algebra and the usual singular cochain complex of a space. We show that this comparison theorem preserves the brace algebra structures. This result gives a structural reason for the recent results establishing fine topological structures on the Hochschild cohomology, and a simple way to derive them from the corresponding properties of cochain complexes.
Revised version of "The bar construction as a Hopf algebra", Dec. 2001