2021/10/22 by Yong‐Geun Oh, Oh, Yong-Geun
Mathematics · #53D05 #53D40 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2110.11726
openalex publication_date 2021/10/22 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/30
We provide a presymplectic characterization of Liouville sectors introduced by Ganatra-Pardon-Shende in terms of the characteristic foliation of the boundary, which we call Liouville σ-sectors. We extend this definition to the case with corners using the presymplectic geometry of null foliations of the coisotropic intersections of transverse coisotropic collection of hypersurfaces which appear in the definition of Liouville sectors with corners. We show that the set of Liouville σ-sectors with corners canonically forms a monoid which provides a natural framework of considering the Künneth-type functors in the wrapped Fukaya category. We identify its automorphism group which enables one to give a natural definition of bundles of Liouville sectors. As a byproduct, we affirmatively answer to a question raised in Question 2.6 in [GPS20], which asks about the optimality of their definition of Liouville sectors [GPS20].