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

Niederkrüger, Klaus

doi:10.2140/agt.2006.6.2473

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

Klaus Niederkrüger

Algebraic & Geometric Topology 6 (2006) 2473–2508

DOI: 10.2140/agt.2006.6.2473

arXiv: math.SG/0607610

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.

Keywords

nonfillable contact manifolds of higher dimension, generalization of overtwistedness

Mathematical Subject Classification 2000

Primary: 53D10, 53R17

Secondary: 53D35

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Publication

Received: 11 September 2006

Revised: 17 November 2006

Accepted: 19 November 2006

Published: 15 December 2006

Authors

Klaus Niederkrüger
Département de Mathématiques Université Libre de Bruxelles, CP 218 Boulevard du Triomphe B-1050 Bruxelles Belgium

Volume 6, issue 5 (2006)