Algebraic & Geometric Topology

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

Klaus Niederkrüger

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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.

Article information

Algebr. Geom. Topol., Volume 6, Number 5 (2006), 2473-2508.

Received: 11 September 2006
Revised: 17 November 2006
Accepted: 19 November 2006
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D10: Contact manifolds, general 53R17
Secondary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]

nonfillable contact manifolds of higher dimension generalization of overtwistedness


Niederkrüger, Klaus. The plastikstufe – a generalization of the overtwisted disk to higher dimensions. Algebr. Geom. Topol. 6 (2006), no. 5, 2473--2508. doi:10.2140/agt.2006.6.2473.

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