Abstract

It is shown that any compact Kahler manifold M gives canonically rise to two strong homotopy algebras, the first one being associated with the Hodge theory of the de Rham complex and the second one with the Hodge theory of the Dolbeault complex. In these algebras the product of two harmonic differential forms is again harmonic. If M happens to be a Calabi-Yau manifold, there exists a third strong homotopy algebra closely related to the Barannikov-Kontsevich extended moduli space of complex structures.

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