On plastikstufe, bordered Legendrian open book and overtwisted contact structures

TL;DR

This paper establishes that embedded plastikstufe and bordered Legendrian open books imply overtwistedness in contact structures across dimensions, providing new criteria for detecting overtwistedness in contact topology.

Contribution

It proves that embedded plastikstufe implies overtwistedness in all dimensions and that bordered Legendrian open books imply overtwistedness specifically in dimension 5, offering new tools for contact topology.

Findings

Embedded plastikstufe implies overtwistedness in any dimension.

Bordered Legendrian open book implies overtwistedness in dimension 5.

Applications to contact fibered sums and open books are discussed.

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.