  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.
