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De Rham cohomology and homotopy Frobenius manifolds. (English) Zbl 1317.58003
In this paper, the authors endow the deRham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. The result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.

MSC:
58A12 de Rham theory in global analysis
14F40 de Rham cohomology and algebraic geometry
53D17 Poisson manifolds; Poisson groupoids and algebroids
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
18G55 Nonabelian homotopical algebra (MSC2010)
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