2024/05/29 by Tony Yue Yu, Yu, Tony Yue, Shao‐Wu Zhang +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2405.19549
openalex publication_date 2024/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct the topological Laplace transform functor from Stokes structures of exponential type to constructible sheaves on \mathbb C with vanishing cohomology. We show that it is compatible with the Fourier transform of D-modules, and induces an equivalence of categories. We give two applications of the construction. First, we study the Fourier transform of B-model nc-Hodge structures associated to Landau-Ginzburg models, and prove the compatibility between the \mathbb Q-structure and the Stokes structure from the connection. Second, we relate the spectral decomposition of nc-Hodge structures to the vanishing cycle decomposition after Fourier transform via choices of Gabrielov paths. This is motivated by the study of the atomic decomposition of A-model nc-Hodge structures associated to smooth projective varieties.