Legendrian Barriers

In a previous work with Felix Schlenk, we showed that an analogue of the phenomenon of Lagrangian barriers holds in the contact framework in S3 : there exist (explicit) Legendrian complexes of arcs in S3 that have short Reeb chords to many Legendrian loops. The aim of this talk is to explain that this phenomenon holds more generally in any prequantization bundle (of arbitrary dimension).