Batalin-Vilkovisky algebras and two-dimensional topological field theories. (English) Zbl 0807.17026

In G. Segal’s approach the two-dimensional topological field theory can be described as a category with sets of morphisms identified with certain moduli spaces. It is shown that in these settings the cohomology of topological field theory in two dimensions is endowed with the structure of a graded commutative algebra \(A\) with the additional operator \(\Delta\) of degree one such that \(\Delta^ 2=0\) and \([\Delta,a]- \Delta(a)\) is a graded derivation of \(A\) for arbitrary \(a\in A\) (Batalin-Vilkovisky algebra). The construction is given in purely topological terms using the language of operads.


17B69 Vertex operators; vertex operator algebras and related structures
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T70 Quantization in field theory; cohomological methods
81R99 Groups and algebras in quantum theory
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