Formality of canonical symplectic complexes and Frobenius manifolds

Abstract

It is shown that the de Rham complex of a symplectic manifold $M$ satisfying the hard Lefschetz condition is formal. Moreover, it is shown that the differential Gerstenhaber-Batalin-Vilkoviski algebra associated to such a symplectic structure gives rise, along the lines explained in the papers of Barannikov and Kontsevich [alg-geom/9710032] and Manin [math/9801006], to the structure of a Frobenius manifold on the de Rham cohomology of $M$.

8 pages, LaTeX, corrected typos and citations

References in corpus (1)

• Three constructions of Frobenius manifolds: a comparative study

Cited by in corpus (12)

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• Algebra of Kodaira-Spencer Gravity and Deformation of Calabi-Yau Manifold
• Harmonic cohomology of symplectic fiber bundles