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.

21 pages, 3 figures. Revised version. Theorem 1.7 has been generalised to arbitrary dimensions and its proof has been simplified

References in corpus (2)

• Lagrangian isotopy of tori in $S^2\times S^2$ and $\mathbb{C}{P}^2$
• Combinatorial Reeb dynamics on punctured contact 3-manifolds