Frobenius manifolds and algebraic integrability

TL;DR

This paper reviews Frobenius manifolds and algebraic integrability, exploring their intersection, introducing new manifold types, and relating Frobenius manifolds of singularities to integrable systems like the Toda chain.

Contribution

It introduces new classes of manifolds called extra special Kaehler and special F-manifolds and studies their relation to algebraic integrability and Frobenius manifolds.

Findings

Frobenius manifolds of simple singularities are nearly dual to the open Toda chain.

New manifold types capture the intersection between Frobenius structures and integrability.

The study reveals structural links between singularities and integrable systems.

Abstract

We give a short review of Frobenius manifolds and algebraic integrability and study their intersection. The simplest case is the relation between the Frobenius manifold of simple singularities, which is almost dual to the integrable open Toda chain. New types of manifolds called extra special Kaehler and special F-manifolds are introduced which capture the intersection.