Formality of canonical symplectic complexes and Frobenius manifolds

Details Formality of canonical symplectic complexes and Frobenius manifolds Formality of canonical symplectic complexes and Frobenius manifolds

1998-05-15

arxiv.org/abs/math/9805072v2

Intern. Math. Research Notices 14 (1998), 727-733

Mathematics

Symplectic Geometry

8 pages, LaTeX, corrected typos and citations

Scientific paper

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 $M$.

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