Symplectically hyperbolic manifolds

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dc.creatorKedra, Jarek
dc.date2007-11-24
dc.date.accessioned2026-07-07T08:44:51Z
dc.date.available2026-07-07T08:44:51Z
dc.descriptionA 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.
dc.description18 pages; preliminary version
dc.identifierhttps://arxiv.org/abs/0711.3828
dc.identifierhttp://arxiv.org/abs/0711.3828
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142801
dc.subjectSymplectic Geometry
dc.subjectGeometric Topology
dc.titleSymplectically hyperbolic manifolds
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