Exact Lagrangians in four‐dimensional symplectisations

Abstract

In this note, we provide explicit constructions of exact Lagrangian embeddings of tori and Klein bottles inside the symplectisation of an overtwisted contact three‐manifold. Note that any closed exact Lagrangian in the symplectisation is displaceable by a Hamiltonian isotopy. We also use positive loops to exhibit elementary examples of topologically linked Legendrians that are dynamically non‐interlinked in the sense of Entov–Polterovich.