Abstract
By a Batalin-Vilkovisky algebra, we mean a graded commutative algebraA, together with an operator Δ:A ⊙→A ⊙+1 such that Δ2 = 0, and [Δ,a]−Δa is a graded derivation ofA for alla∈A. In this article, we show that there is a natural structure of a Batalin-Vilkovisky algebra on the cohomology of a topological conformal field theory in two dimensions. We make use of a technique from algebraic topology: the theory of operads.
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Communicated by A. Jaffe
The author is partially supported by a fellowship of the Sloan Foundation and a research grant of the NSF
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Getzler, E. Batalin-Vilkovisky algebras and two-dimensional topological field theories. Commun.Math. Phys. 159, 265–285 (1994). https://doi.org/10.1007/BF02102639
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DOI: https://doi.org/10.1007/BF02102639