Homotopy Gerstenhaber algebras and topological field theory
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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.
29 pages, to appear in "Operads: Proceedings of Renaissance Conferences", J.-L. Loday, J. Stasheff, and A.A. Voronov, eds., Contemp. Math., AMS, Providence, RI (1996). In the resubmitted version, a few inaccuracies corrected
29 pages, to appear in "Operads: Proceedings of Renaissance Conferences", J.-L. Loday, J. Stasheff, and A.A. Voronov, eds., Contemp. Math., AMS, Providence, RI (1996). In the resubmitted version, a few inaccuracies corrected