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

Primary: 53D10, 53R17

Secondary: 53D35

References

Forward citations

Publication

Received: 11 September 2006
Revised: 17 November 2006
Accepted: 19 November 2006
Published: 15 December 2006

Authors