De Rham cohomology and homotopy Frobenius manifolds

TL;DR

This paper introduces a natural homotopy Frobenius manifold structure on the de Rham cohomology of Poisson and Jacobi manifolds, utilizing a minimal model theorem and a novel Hodge degeneration condition.

Contribution

It provides the first construction of homotopy Frobenius structures on de Rham cohomology for these manifolds, expanding the understanding of their algebraic and geometric properties.

Findings

Established a minimal model theorem for multicomplexes.

Introduced a new Hodge degeneration condition.

Constructed homotopy Frobenius manifold structures on cohomology.

Abstract

We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.