  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.
