Strongly homotopy algebras of a Kähler manifold

1998/09/30 by S. A. Merkulov
Mathematics · #math.AG #math.AT #math.DG #math.QA

paper · pdf

published as Internat. Math. Res. Notices (1999), no.3, 153--164 · Correction

arxiv created 2001/08/13 · arxiv updated 2009/11/30

Abstract

It is shown that any compact Kähler manifold M gives canonically rise to two strongly 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 strongly homotopy algebra closely related to the Barannikov-Kontsevich extended moduli space of complex structures.

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