Analytic theory of Legendre-type transformations for a Frobenius manifold

2023/11/07 by Dixiong Yang, Yang, Di · 1 citation
Chemistry · Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality

paper · pdf · doi:10.48550/arxiv.2311.04200

openalex publication_date 2023/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be an n-dimensional Frobenius manifold. Fix κ∈\1,…,n\. Assuming certain invertibility, Dubrovin introduced the Legendre-type transformation S_κ, which transforms M to an n-dimensional Frobenius manifold S_κ(M). In this paper, we show that these S_κ(M) share the same monodromy data at the Fuchsian singular point of the Dubrovin connection, and that for the case when M is semisimple they also share the same Stokes matrix and the same central connection matrix. A straightforward application of the monodromy identification is the following: if we know the monodromy data of some semisimple Frobenius manifold M, we immediately obtain those of its Legendre-type transformations. Another application gives the identification between the κth partition function of a semisimple Frobenius manifold M and the topological partition function of S_κ(M).

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