Batalin-Vilkovisky algebras and two-dimensional topological field theories

Abstract

By a Batalin-Vilkovisky algebra, we mean a graded commutative algebra A, together with an operator Δ:A⊙→A⊙+1 such that Δ2 = 0, and [Δ, a]-Δa is a graded derivation of A for all a∈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. © 1994 Springer-Verlag.