2014/01/23 by Kaileung Chan, Naichung Conan Leung, Chan, Kaileung +3
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1401.5867
openalex publication_date 2014/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Wedge product on deRham complex of a Riemannian manifold M can be pulled back to H^*(M) via explicit homotopy, constructed using Green's operator, to give higher product structures. We prove Fukaya's conjecture which suggests that Witten deformation of these higher product structures have semiclassical limits as operators defined by counting gradient flow trees with respect to Morse functions, which generalizes the remarkable Witten deformation of deRham differential from a statement concerning homology to one concerning real homotopy type of M. Various applications of this conjecture to mirror symmetry are also suggested by Fukaya.