The Abhary-Kontsevich Correspondence: Modeling Ore Systems via Homological Mirror Symmetry and Lagrangian Floer Homology

Abstract: Traditional metallogeny treats structural geometry and geochemistry as distinct domains. We propose a unified field theory based on Homological Mirror Symmetry (HMS). By modeling the mineralized crust as a generalized Calabi-Yau ۳-fold, we postulate an equivalence between the symplectic geometry of fault networks (A-Model) and the complex geometry of hydrothermal potentials (B-Model). Utilizing the framework of Kapustin et al. (۲۰۰۸) and the Lagrangian Floer cohomology discussed by Ekholm (۲۰۱۱), we derive the Abhary-Kontsevich Correspondence. We show that ore bodies are not merely physical volumes but intersection points of Lagrangian submanifolds in the moduli space of fluid pathways. Furthermore, we apply the Fourier-Mukai transform (Chan, ۲۰۱۳) to convert surface geochemical data into deep-seated structural predictions, defining the "Abhary-Floer Index" as a deterministic measure of mineral endowment.

کلیدواژه ها:

Homological Mirror Symmetry ، Fukaya Categories ، Lagrangian Floer Homology ، Calabi-Yau Manifolds ، Maslov Index ، Fourier-Mukai Transform