The plastikstufe - a generalization of the overtwisted disk to higher dimensions

Abstract

In this article, we give a first prototype-definition of overtwistedness in higher dimensions. According to this definition, a contact manifold is called "overtwisted" if it contains a "plastikstufe", a submanifold foliated by the contact structure in a certain way. In three dimensions the definition of the plastikstufe is identical to the one of the overtwisted disk. The main justification for this definition lies in the fact that the existence of a plastikstufe implies that the contact manifold does not have a (semipositive) symplectic filling.

This is the version published by Algebraic & Geometric Topology on 15 December 2006

References in corpus (2)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• A class of non-fillable contact structures

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