2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79273Manifolds with a commutative and associative multiplication on the tangent bundle are called F-manifolds if a unit field exists and the multiplication satisfies a natural integrability condition. They are studied here. They are closely related to discriminants and Lagrange maps. Frobenius manifolds are F-manifolds. As an application a conjecture of Dubrovin on Frobenius manifolds and Coxeter groups is proved.88 pages, AMS-LaTeXAlgebraic GeometryQuantum AlgebraSymplectic Geometrytext