Merkulov, S. A. Formality of canonical symplectic complexes and Frobenius manifolds. (English) Zbl 0931.58002 Int. Math. Res. Not. 1998, No. 14, 727-733 (1998). It was shown by S. Barannikov and M. Kontsevich [Int. Math. Res. Not. 1998, No. 4, 201-215 (1998; Zbl 0914.58004)] that the formal moduli space of solutions to the Maurer-Cartan equations, modulo gauge equivalence associated to a very special class of differential Gerstenhaber-Batalin-Vilkovisky (dGBV) algebras, carries the natural structure of a Frobenius manifold.To the author’s knowledge, only one example of such a special dGBV algebra was known: the one constructed out of the Dolbeault complex of an arbitrary Calabi-Yau manifold by Barannikov and Kontsevich [loc. cit.].In this note, we produce another example of a special dGBV-algebra, namely, the one associated with an arbitrary symplectic manifold \((M,\omega)\) satisfying the hard Lefschetz condition which says that the cup product \[ [\omega^k]: H^{m-k}(M)\to H^{m+ k}(M) \] is an isomorphism for any \(k\leq m=1/2\dim M\). Applying then the machinery developed by S. Barannikov and M. Kontsevich [loc. cit.] and Yu. I. Manin to the moduli space of solutions of the associated Maurer-Cartan equation, we get a structure of a Frobenius manifold on the de Rham cohomology of \(M\). Cited in 1 ReviewCited in 31 Documents MSC: 58A12 de Rham theory in global analysis 58H15 Deformations of general structures on manifolds 58J10 Differential complexes Keywords:differential Gerstenhaber-Batalin-Vilkovisky algebras; symplectic manifold; Maurer-Cartan equation; Frobenius manifold; deRham cohomology Citations:Zbl 0914.58004 PDFBibTeX XMLCite \textit{S. A. Merkulov}, Int. Math. Res. Not. 1998, No. 14, 727--733 (1998; Zbl 0931.58002) Full Text: DOI arXiv