On plastikstufe, bordered Legendrian open book and overtwisted contact structures

Abstract

In this paper we prove the presence of an embedded plastikstufe implies overtwistedness of the contact structure in any dimension. Moreover, we show in dimension 5 that the presence of an embedded bordered Legendrian open book (bLob) also implies overtwistedness. Applications of these criteria to certain (contact) fibered connected sums and open books are discussed.

final version; substantial revisions; to appear in the Journal of Topology

References in corpus (2)

• Right-veering diffeomorphisms of compact surfaces with boundary II
• The plastikstufe - a generalization of the overtwisted disk to higher dimensions

Cited by in corpus (3)

• On some examples and constructions of contact manifolds
• Examples of non-trivial contact mapping classes for overtwisted contact manifolds in all dimensions
• An overtwisted convex hypersurface in higher dimensions