Getzler, E. Batalin-Vilkovisky algebras and two-dimensional topological field theories. (English) Zbl 0807.17026 Commun. Math. Phys. 159, No. 2, 265-285 (1994). 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. Reviewer: S.Khoroshkin (Moskva) Cited in 6 ReviewsCited in 126 Documents MSC: 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 Keywords:Batalin-Vilkovisky algebra; two-dimensional topological field theory; operads × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Arnold, V.I.: The cohomology ring of the colored braid group. Mat. Zametki5, 227–231 (1969) [2] Beilinson, A., Ginzburg, V.: Infinitesimal structures of moduli space ofG-bundles. Duke Math. J.66, 63–74 (1992) · Zbl 0763.32011 [3] Birman, J.S.: Braids, links and mapping class groups. Ann. Math. Studies, no. 82, Princeton, NJ: Princeton U. Press 1974 [4] Boardman, J.M., Vogt, R.M.: Homotopy invariant algebraic structures on topological spaces. 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