Monoid of Liouville sectors with corners and its intrinsic characterization
Year: 2021
Type: preprint
Abstract: We provide a $G$-structure type characterization of Liouville sectors introduced by Ganatra-Pardon-Shende [GPS17] in terms of the characteristic foliation of the boundary, which we call Liouville $\sigma$-sectors. We extend this definition to the case with corners using the presymplectic geometry of null foliations of the coisotropic intersections of clean coisotropic collection of hypersurfaces which appear in the definition of Liouville sectors with corners. We give the definition of the structure of Liouville sectors with corners as a substructure of the monoid of manifolds with boundary and corners, and identify its automorphism group which enables us to give a natural definition of bundles of Liouville sectors. Then for a given Liouville $\sigma$-sector with corners $(M,\lambda)$, we introduce the class of gradient-sectorial Lagrangian submanifolds and the notion of sectorial almost complex structures the pairs of which are amenable to the strong maximum principle. In particular the wrapped Fukaya category generated by gradient-sectorial Lagrangian branes on Liouville ($\sigma$-)sectors with corners becomes monoidal in the chain level under the monoidal product of manifolds with corners. We also affirmatively answer to Question 2.6 raised in [GPS17].
Source: arXiv (Cornell University)
Author: Yong‐Geun Oh
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3210776399