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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The plastikstufe – a generalization of the overtwisted disk to higher dimensions

Klaus Niederkrüger

Algebraic & Geometric Topology 6 (2006) 2473–2508

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