2007/11/24 by Jarek Kędra, Kedra, Jarek · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.0711.3828
openalex publication_date 2007/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms. The main results are: * If a symplectic form represents a bounded cohomology class then it is hyperbolic. * The symplectic hyperbolicity is equivalent to a certain isoperimetric inequality. * The fundamental group of symplectically hyperbolic manifold is non-amenable. We also construct hyperbolic symplectic forms on certain bundles and Lefschetz fibrations, discuss the dependenc of the symplectic hyperbolicity on the fundamental group and discuss some properties of the group of symplectic diffeomorphisms of a symplectically hyperbolic manifold.