Frobenius 3-folds via singular flat 3-webs (Q352381)

A Frobenius manifold is a manifold where each tangent space has a multiplicative structure generalizing a Frobenius algebra. Frobenius manifolds are important in the study of quantum cohomology and Gromov-Witten invariants. A web on an \(n\)-dimensional Riemannian manifold is a collection of \(n\) codimensions-one foliations that are transverse and orthogonal. This paper begins by describing a natural web that one may define on a \(3\)-dimensional Frobenius manifold when the tangent space is semi-simple. It recalls a number of properties of such webs. The main point of the paper is that this procedure may be turned around. Given a suitable \(3\)-web one may define the germ of a \(3\)-dimensional Frobenius manifold.