Lagrangian isotopies and symplectic function theory

  • Michael Entov

    Technion - Israel Institute of Technology, Haifa, Israel
  • Yaniv Ganor

    Tel Aviv University, Israel
  • Cedric Membrez

    Tel Aviv University, Israel


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 this article

Michael Entov, Yaniv Ganor, Cedric Membrez, Lagrangian isotopies and symplectic function theory. Comment. Math. Helv. 93 (2018), no. 4, pp. 829–882

DOI 10.4171/CMH/451