2016/10/30 by Michael Entov, Entov, Michael, Yaniv Ganor +3 · 1 citation
Mathematics · #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG
paper · pdf · doi:10.48550/arxiv.1610.09631
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
arxiv created 2018/01/01 · arxiv updated 2018/01/03
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.