C⁰-rigidity of Lagrangian submanifolds and punctured holomorphic discs in the cotangent bundle

2017/12/18 by Membrez, Cedric, Opshtein, Emmanuel
#53D05 53D12 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1712.06404

Abstract

Our main result is the C⁰-rigidity of the area spectrum and the Maslov class of Lagrangian submanifolds. This relies on the existence of punctured pseudoholomorphic discs in cotangent bundles with boundary on the zero section, whose boundaries represent any integral homology class. We discuss further applications of these punctured discs in symplectic geometry.

Related

• Punctured holomorphic curves and Lagrangian embeddings
• C⁰-characterization of symplectic and contact embeddings and\n Lagrangian rigidity
• Maslov class rigidity for Lagrangian submanifolds via Hofer's geometry
• Symplectic Rigidity of Fibers in Cotangent Bundles of Open Riemann Surfaces
• Symplectic displacement energy for exact Lagrangian immersions