Punctured holomorphic curves and Lagrangian embeddings

Abstract

We use a neck stretching argument for holomorphic curves to produce symplectic disks of small area and Maslov class with boundary on Lagrangian submanifolds of nonpositive curvature. Applications include the proof of Audin's conjecture on the Maslov class of Lagrangian tori in linear symplectic space, the construction of a new symplectic capacity, obstructions to Lagrangian embeddings into uniruled symplectic manifolds, a quantitative version of Arnold's chord conjecture, and estimates on the size of Weinstein neighbourhoods. The main technical ingredient is transversality for the relevant moduli spaces of punctured holomorphic curves with tangency conditions.

arXiv comment61 pages, 3 (LaTeX) figures, reference added

References in corpus (7)

• Compactness results in Symplectic Field Theory
• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Rigidity and uniruling for Lagrangian submanifolds
• Do uniruled six-manifolds contain Sol Lagrangian submanifolds?
• Geometric transversality in higher genus Gromov-Witten theory
• The asymptotics of ECH capacities
• On the strict Arnold chord property and coisotropic submanifolds of complex projective space

Cited by in corpus (4)

• Floer theory and flips
• Fukaya algebras via stabilizing divisors
• On the strict Arnold chord property and coisotropic submanifolds of complex projective space
• Rational Quantum Cohomology of Steenrod Uniruled Manifolds