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.