  Batalin-Vilkovisky algebras are a new type of algebraic structure on graded
vector spaces, which first arose in the work of Batalin and Vilkovisky on gauge
fixing in quantum field theory. In this article, we show that there is a
natural structure of a Batalin-Vilkovisky algebra on the cohomology of a
topological field theory in two dimensions.
  Lian and Zuckerman have constructed this Batalin-Vilkovisky structure, in the
setting of topological chiral field theories, and shown that the structure is
non-trivial in two-dimensional string theory. Our approach is to use algebraic
topology, whereas their proofs have a more algebraic character.
