Cyclic $BV_\infty$ algebra and Frobenius manifold

TL;DR

This paper constructs Frobenius manifolds from cyclic BV_infinity algebras with applications to Jacobi and Hermitian manifolds, generalizing existing results in the field.

Contribution

It introduces a new method to build Frobenius manifolds from cyclic BV_infinity algebras under specific conditions, extending previous work to broader classes of manifolds.

Findings

Constructed Frobenius manifolds from cyclic BV_infinity algebras.

Applied the construction to Jacobi and Hermitian manifolds.

Generalized known results in the literature.

Abstract

We describe the construction of Frobenius manifold out of a cyclic (commutative) $BV_\infty$ algebra $(A,\Delta)$ under the assumption of a Hodge-to-de Rham degeneration property and the existence of a compatible homotopy retract of $A$ onto its cohomology. We then apply it to Jacobi manifolds and Hermitian manifolds, generalizing known results in literature.