Lagrangian isotopies and symplectic function theory

Michael Entov, Yaniv Ganor, Cedric Membrez

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish
Pages (from-to)829-882
Number of pages54
JournalCommentarii Mathematici Helvetici
Volume93
Issue number4
DOIs
StatePublished - 2018

Keywords

  • Lagrangian isotopy
  • Lagrangian submanifold
  • Poisson bracket
  • Symplectic function theory
  • Symplectic manifold

ASJC Scopus subject areas

  • General Mathematics

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