Communications in Mathematical Physics

, Volume 159, Issue 2, pp 265–285

Batalin-Vilkovisky algebras and two-dimensional topological field theories

  • E. Getzler

DOI: 10.1007/BF02102639

Cite this article as:
Getzler, E. Commun.Math. Phys. (1994) 159: 265. doi:10.1007/BF02102639


By a Batalin-Vilkovisky algebra, we mean a graded commutative algebraA, together with an operator Δ:AA⊙+1 such that Δ2 = 0, and [Δ,a]−Δa is a graded derivation ofA for allaA. 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.

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • E. Getzler
    • 1
  1. 1.Department of MathematicsMITCambridgeUSA