Lagrangian submanifolds: open Gromov-Witten theory and Mirror Symmetry
Applications of Lie theory in the symplectic and hermitian geometry of homogeneous...
Lefschetz fibrations, Lie groupoids and noncommutative geometry
| Full text | |
| Author(s): |
Shelukhin, Egor
;
Tonkonog, Dmitry
;
Vianna, Renato
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Journal of Topology; v. 17, n. 4, p. 56-pg., 2024-12-01. |
| Abstract | |
Symplectic flux measures the areas of cylinders swept in the process of a Lagrangian isotopy. We study flux via a numerical invariant of a Lagrangian submanifold that we define using its Fukaya algebra. The main geometric feature of the invariant is its concavity over isotopies with linear flux. We derive constraints on flux, Weinstein neighbourhood embeddings and holomorphic disk potentials for Gelfand-Cetlin fibres of Fano varieties in terms of their polytopes. We also describe the space of fibres of almost toric fibrations on the complex projective plane up to Hamiltonian isotopy, and provide other applications. (AU) | |
| FAPESP's process: | 24/01351-6 - Lagrangian submanifolds: open Gromov-Witten theory and Mirror Symmetry |
| Grantee: | Renato Ferreira de Velloso Vianna |
| Support Opportunities: | Research Grants - Young Investigators Grants |