# A FLOER HOMOLOGY FOR EXACT CONTACT EMBEDDINGS

@article{Cieliebak2007AFH, title={A FLOER HOMOLOGY FOR EXACT CONTACT EMBEDDINGS}, author={Kai Cieliebak and Urs Frauenfelder}, journal={Pacific Journal of Mathematics}, year={2007}, volume={239}, pages={251-316} }

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.

## 102 Citations

Floer Homology and Rabinowitz-Floer homology

- Mathematics
- 2016

Let (M,ω) be a closed symplectic 2n-dimensional manifold that is symplectically aspherical with vanishing first Chern class. The (weak) Arnold conjecture states that the number of contractible…

Equivariant symplectic homology and multiple closed Reeb orbits

- Mathematics
- 2013

We study the existence of multiple closed Reeb orbits on some contact manifolds by means of $S^1$-equivariant symplectic homology and the index iteration formula. It is proved that a certain class of…

Continuation homomorphism in Rabinowitz Floer homology for symplectic deformations

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2011

Abstract Will J. Merry computed Rabinowitz Floer homology above Mañé's critical value in terms of loop space homology in [14] by establishing an Abbondandolo–Schwarz short exact sequence. The purpose…

Translated points on hypertight contact manifolds

- MathematicsJournal of Topology and Analysis
- 2018

A contact manifold admitting a supporting contact form without contractible Reeb orbits is called hypertight. In this paper we construct a Rabinowitz–Floer homology associated to an arbitrary…

Rabinowitz–Floer homology for superquadratic Dirac equations on compact spin manifolds

- Mathematics
- 2013

In this paper, we investigate the properties of a semilinear problem on a spin manifold involving the Dirac operator through the construction of Rabinowitz–Floer homology groups. We give several…

Leaf-wise intersections and Rabinowitz Floer homology

- Mathematics
- 2010

In this paper we explain how critical points of a particular perturbation of the Rabinowitz action functional give rise to leaf-wise intersection points in hypersurfaces of restricted contact type.…

Handle attaching in symplectic topology-a second glance

- Mathematics
- 2016

We give a corrected proof of Cieliebaks important result on the invariance of symplectic homology under handle attachment. This paper is partly based on the authors PhD-thesis, during which he was…

A Variational Approach to Givental’s Nonlinear Maslov Index

- Mathematics
- 2011

In this article we consider a variant of Rabinowitz Floer homology in order to define a homological count of discriminant points for paths of contactomorphisms. The growth rate of this count can be…

Künneth formula in Rabinowitz Floer homology

- Mathematics
- 2010

Rabinowitz Floer homology has been investigated on submanifolds of contact type. The contact condition, however, is quite restrictive. For example, a product of contact hypersurfaces is rarely of…

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