2024/09/23 by Gao Yuan, Gao, Yuan
Mathematics · #14B20 #16E40 #18G70 #53D37 #Advanced Topics in Algebra #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2409.14966
openalex publication_date 2024/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a stopped Liouville manifold arising from a Liouville sector, we construct a symplectic analogue of the formal neighborhood of the stop on the level of Fukaya categories. This geometric construction is performed via Floer-theoretic methods by allowing wrappings in the negative direction. On the other hand, inspired by homological mirror symmetry for pairs, where the mirror is the formal neighborhood of a divisor in an ambient projective variety, there is a different approach by taking a `categorical formal completion' introduced by Efimov. Our main results establishes equivalence of these two approaches, confirms computability of this new type of Floer theory by categorical and algebraic means, and indicates contributions from and to computations in homological mirror symmetry.