A Floer homology for exact contact embeddings

Kai Cieliebak and Urs Adrian Frauenfelder

Vol. 239 (2009), No. 2, 251–316

DOI: 10.2140/pjm.2009.239.251

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 ℂⁿ.

Keywords

contact manifolds, Floer homology, Rabinowitz action functional

Mathematical Subject Classification 2000

Primary: 53D10, 53D40

Milestones

Received: 4 October 2007

Revised: 24 September 2008

Accepted: 10 November 2008

Published: 27 November 2008

Correction: 1 February 2011