A Floer homology for exact contact embeddings

TL;DR

This paper develops Floer homology for a specific action functional, proving a vanishing theorem and applying it to show certain contact embeddings cannot exist, extending Gromov's classical result.

Contribution

It introduces Floer homology for Rabinowitz's action functional and applies it to prove non-existence of certain contact embeddings, generalizing known Lagrangian embedding results.

Findings

Vanishing theorem for the Floer homology constructed

No displaceable exact contact embeddings of certain spheres

Extension of Gromov's non-embedding result

Abstract

In this paper we construct the Floer homology for an action functional which was introduced by Rabinowitz and prove a vanishing theorem. As an application, we show that there are no displaceable exact contact embeddings of the unit cotangent bundle of a sphere of dimension greater than three into a convex exact symplectic manifold with vanishing first Chern class. This generalizes Gromov's result that there are no exact Lagrangian embeddings of a sphere into a complex vector space.