Geodesic
The plastikstufe – a generalization of the overtwisted disk to higher dimensions
Niederkrüger, Klaus1
1Département de Mathématiques, Université Libre de Bruxelles, CP 218, Boulevard du Triomphe, B-1050 Bruxelles, Belgium
Algebraic and Geometric Topology, Tome 6 (2006) no. 5, pp. 2473-2508
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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.

DOI : 10.2140/agt.2006.6.2473
Keywords: nonfillable contact manifolds of higher dimension, generalization of overtwistedness

Niederkrüger, Klaus  1

1 Département de Mathématiques, Université Libre de Bruxelles, CP 218, Boulevard du Triomphe, B-1050 Bruxelles, Belgium 
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Niederkrüger, Klaus. The plastikstufe – a generalization of the overtwisted disk to higher dimensions. Algebraic and Geometric Topology, Tome 6 (2006) no. 5, pp. 2473-2508. doi: 10.2140/agt.2006.6.2473

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