Batalin-Vilkovisky algebras and two-dimensional topological field theories

E. Getzler

doi:10.1007/BF02102639

Batalin-Vilkovisky algebras and two-dimensional topological field theories

E. Getzler^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

174 Scopus citations

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.

Original language	English (US)
Pages (from-to)	265-285
Number of pages	21
Journal	Communications in Mathematical Physics
Volume	159
Issue number	2
DOIs	https://doi.org/10.1007/BF02102639
State	Published - Jan 1994

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02102639

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AB - 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.

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Batalin-Vilkovisky algebras and two-dimensional topological field theories

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