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2006 The plastikstufe – a generalization of the overtwisted disk to higher dimensions
Klaus Niederkrüger
Algebr. Geom. Topol. 6(5): 2473-2508 (2006). DOI: 10.2140/agt.2006.6.2473

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.

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Klaus Niederkrüger. "The plastikstufe – a generalization of the overtwisted disk to higher dimensions." Algebr. Geom. Topol. 6 (5) 2473 - 2508, 2006. https://doi.org/10.2140/agt.2006.6.2473

Information

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

zbMATH: 1129.53056
MathSciNet: MR2286033
Digital Object Identifier: 10.2140/agt.2006.6.2473

Subjects:
Primary: 53D10, 53R17
Secondary: 53D35

Rights: Copyright © 2006 Mathematical Sciences Publishers

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Vol.6 • No. 5 • 2006
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