2022/11/07 by Yoosik Kim, Kim, Yoosik, Siu-Cheong Lau +3 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2211.03558
openalex publication_date 2022/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive a Floer theoretical SYZ mirror for an equilateral and generic polygon space. The disk potential function of the monotone torus fiber of the caterpillar bending system is calculated by computing non-trivial open Gromov--Witten invariants from the structural result of the monotone Fukaya category, the topology of fibers of completely integrable systems, and toric degenerations. Then, combining the result with the work of Nohara--Ueda [NU20] and Marsh--Rietsch [MR20], we obtain the disk potential functions of bending systems and produce a mirror cluster variety of type A without frozen variables via Lagrangian Floer theory.