Geometry of symplectic flux and Lagrangian torus fibrations
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.
Authors
- Dmitry Tonkonog
- Egor Shelukhin (ORCID: https://orcid.org/0000-0001-8092-5668)
- Renato Vianna (ORCID: https://orcid.org/0000-0003-4149-1865)
Institutions
- Universidade de São Paulo (BR)
- Université de Montréal (CA)
- Universidade São Francisco (BR)
- University of California, Berkeley (US)
Publication Details
- Journal
- Journal of Topology
- Published
- 2024-10-22
- DOI
- https://doi.org/10.1112/topo.70002
- Citations
- 8
- Primary Topic
- Geometric and Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 2.02
Funders
- National Science Foundation
- Simons Foundation
- United States Pharmacopeia
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
- Instituto Serrapilheira