Formality of canonical symplectic complexes and Frobenius manifolds

1998/05/19 by S. A. Merkulov · 4 citations
Mathematics · #math.SG

paper · pdf

published as Intern. Math. Research Notices 14 (1998), 727-733 · 8 pages, LaTeX, corrected typos and citations

arxiv created 1998/05/19 · arxiv updated 2009/11/30

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.

Cited by

• Hodge decomposition and Hard Lefschetz Condition on almost Kähler manifolds
• Symplectic solvmanifolds not satisfying the hard-Lefschetz condition
• Symplectic non-Kähler manifolds with and without the Hard Lefschetz Condition
• Representations of Hamiltonian vector fields on a torus

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