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

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

2006-07-25

arxiv.org/abs/math/0607610v2

Algebr. Geom. Topol. 6 (2006) 2473-2508

Mathematics

Symplectic Geometry

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

Scientific paper

10.2140/agt.2006.6.2473

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.

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