Lagrangian isotopies and symplectic function theory
| Autor: | Entov, Michael, Ganor, Yaniv, Membrez, Cedric |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study two related invariants of Lagrangian submanifolds in symplectic manifolds. For a Lagrangian torus these invariants are functions on the first cohomology of the torus. The first invariant is of topological nature and is related to the study of Lagrangian isotopies with a given Lagrangian flux. More specifically, it measures the length of straight paths in the first cohomology that can be realized as the Lagrangian flux of a Lagrangian isotopy. The second invariant is of analytical nature and comes from symplectic function theory. It is defined for Lagrangian submanifolds admitting fibrations over a circle and has a dynamical interpretation. We partially compute these invariants for certain Lagrangian tori. Comment: The statements and the proofs of the rigidity theorems for Lagrangian tori in C^n revised; other minor changes. Accepted for publication in Commentarii Mathematici Helvetici |
| Databáze: | arXiv |
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