On a class of integrable deformations of the integrable hierarchy of topological type associated to a semisimple Frobenius manifold

2025/11/10 by Liu, Si-Qi, Rossi, Paolo, Yang, Di +1
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · doi:10.48550/arxiv.2511.06984

openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

Given a semisimple Frobenius manifold, we construct a class of integrable deformations of its hierarchy of topological type. We show that these integrable deformations have polynomial tau-structures, and conjecture that for the one-dimensional Frobenius manifold they give a universal object for integrable deformations of the Riemann--Hopf hierarchy having a tau-structure.

Citations

• Mapping partition functions
• The Virasoro-like Algebra of a Frobenius Manifold
• Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs
• The curvature of a Hessian metric
• On almost duality for Frobenius manifolds
• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• Gromov - Witten invariants and quantization of quadratic hamiltonians
• Hodge integrals and Gromov-Witten theory
• Frobenius Manifolds And Virasoro Constraints
• Geometry of 2d topological field theories

Related

• Generalized Frobenius Manifolds with Non-flat Unity and Integrable Hierarchies
• Frobenius Manifolds, Spectral Curves, and Integrable Hierarchies
• Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs
• The extended Ablowitz-Ladik hierarchy and a generalized Frobenius manifold
• Unfoldings of meromorphic connections and a construction of Frobenius manifolds