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Abstract
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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.
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Keywords
contact manifolds, Floer homology,
Rabinowitz action functional
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Mathematical Subject Classification
Primary: 53D10, 53D40
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Milestones
Received: 4 October 2007
Revised: 24 September 2008
Accepted: 10 November 2008
Published: 27 November 2008
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