Lagrangian isotopies and symplectic function theory
Abstract
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.
Cite
@article{arxiv.1610.09631,
title = {Lagrangian isotopies and symplectic function theory},
author = {Michael Entov and Yaniv Ganor and Cedric Membrez},
journal= {arXiv preprint arXiv:1610.09631},
year = {2018}
}
Comments
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