Distinguishing between exotic symplectic structures

Abstract

We investigate the uniqueness of so-called exotic structures on certain exact symplectic manifolds by looking at how their symplectic properties change under small nonexact deformations of the symplectic form. This allows us to distinguish between two examples based on those found in \cite{maydanskiy,maydanskiyseidel}, even though their classical symplectic invariants such as symplectic cohomology vanish. We also exhibit, for any $n$, an exact symplectic manifold with $n$ distinct but exotic symplectic structures, which again cannot be distinguished by symplectic cohomology.

33 pages, 6 figures. Final version, accepted by Journal of Topology

References in corpus (5)

• Functors and Computations in Floer homology with Applications Part II
• Altering symplectic manifolds by homologous recombination
• Exotic symplectic manifolds from Lefschetz fibrations
• Effect of Legendrian Surgery
• Open strings, Lagrangian conductors and Floer functor

Cited by in corpus (6)

• Legendrian Fronts for Affine Varieties
• Maximal contact and symplectic structures
• Subflexible symplectic manifolds
• Invariance of symplectic cohomology and twisted cotangent bundles over surfaces
• Non-standard Symplectic Structures via Symplectic Cohomology
• On the Theory of Stein Manifolds