  We prove that the BRST complex of a topological conformal field theory is a
homotopy Gerstenhaber algebra, as conjectured by Lian and Zuckerman in 1992. We
also suggest a refinement of the original conjecture for topological vertex
operator algebras. We illustrate the usefulness of our main tools, operads and
"string vertices" by obtaining new results on Vassiliev invariants of knots and
double loop spaces.
