The Maslov class of Lagrangian tori and quantum products in Floer cohomology

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Abstract

We use Floer cohomology to prove the monotone version of a conjecture of Audin: the minimal Maslov number of a monotone Lagrangian torus in ℝ 2n is 2. Our approach is based on the study of the quantum cup product on Floer cohomology and in particular the behavior of Oh's spectral sequence with respect to this product. As further applications, we prove existence of holomorphic disks with boundaries on Lagrangians as well as new results on Lagrangian intersections.

Original languageEnglish
Pages (from-to)57-75
Number of pages19
JournalJournal of Topology and Analysis
Volume2
Issue number1
DOIs
StatePublished - Mar 2010
Externally publishedYes

Keywords

  • Audin conjecture
  • Floer cohomology
  • Lagrangian submanifold
  • Maslov index
  • Oh's spectral sequence
  • quantum cup product

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