Infinite-Dimensional Frobenius Manifolds for 2+1 Integrable Systems

Abstract

We introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/infinity respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobenius manifold.

29 pages; to appear in Math. Ann

References in corpus (5)

• Combinatorics of dispersionless integrable systems and universality in random matrix theory
• The multicomponent 2D Toda hierarchy: dispersionless limit
• Differential Fay identities and auxiliary linear problem of integrable hiearchies
• Normal matrix models, dbar-problem, and orthogonal polynomials on the complex plane
• Equivariant orbifold structures on the projective line and integrable hierarchies