2025/08/03 by Gorapada Bera, Bera, Gorapada
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2508.01899
This article develops the deformation theory of asymptotically cylindrical (ACyl) associative submanifolds in ACyl G2-manifolds, laying the foundation for the gluing of ACyl associative submanifolds in twisted connected sum G2-manifolds presented by the author in [Ber22]. We study the moduli space of ACyl associative submanifolds with a fixed asymptotic holomorphic curve and a fixed rate, as well as the moduli space where this asymptotic data is allowed to vary, each endowed with a natural topology. We compute their virtual dimensions and show that in the best-case scenario, the latter embeds as a Lagrangian submanifold in the moduli space of holomorphic curves of the limiting Calabi-Yau 3-fold. These results may also be of independent interest for future.