# Rabinowitz Floer homology and symplectic homology

@article{Cieliebak2009RabinowitzFH,
title={Rabinowitz Floer homology and symplectic homology},
author={Kai Cieliebak and Urs Frauenfelder and Alexandru Oancea},
journal={arXiv: Symplectic Geometry},
year={2009}
}
• Published 4 March 2009
• Mathematics
• arXiv: Symplectic Geometry
The Rabinowitz-Floer homology groups $RFH_*(M,W)$ are associated to an exact embedding of a contact manifold $(M,\xi)$ into a symplectic manifold $(W,\omega)$. They depend only on the bounded component $V$ of $W\setminus M$. We construct a long exact sequence in which symplectic cohomology of $V$ maps to symplectic homology of $V$, which in turn maps to Rabinowitz-Floer homology $RFH_*(M,W)$, which then maps to symplectic cohomology of $V$. We compute $RFH_*(ST^*L,T^*L)$, where $ST^*L$ is the…

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## References

SHOWING 1-10 OF 32 REFERENCES
A survey of Floer homology for manifolds with contact type boundary or symplectic homology
• A. Oancea
• Mathematics
Ensaios Matemáticos
• 2004
The purpose of this paper is to give a survey of the various versions of Floer homology for manifolds with contact type boundary that have so far appeared in the literature. Under the name of
Functors and Computations in Floer Homology with Applications, I
Abstract. This paper is concerned with Floer cohomology of manifolds with contact type boundary. In this case, there is no conjecture on this ring, as opposed to the compact case, where it is
Symplectic topology of Mañé's critical values
• Mathematics
• 2009
We study the dynamics and symplectic topology of energy hypersurfaces of mechanical Hamiltonians on twisted cotangent bundles. We pay particular attention to periodic orbits, displaceability,
On the Floer homology of cotangent bundles
• Mathematics
• 2004
This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle of a compact orientable manifold M. The first result is a new uniform estimate
An exact sequence for contact- and symplectic homology
• Mathematics
• 2009
A symplectic manifold W with contact type boundary M=∂W induces a linearization of the contact homology of M with corresponding linearized contact homology HC(M). We establish a Gysin-type exact
Floer homology and Novikov rings
• Mathematics
• 1995
We prove the Arnold conjecture for compact symplectic manifolds under the assumption that either the first Chern class of the tangent bundle vanishes over π2(M) or the minimal Chern number is at
The homology theory of the closed geodesic problem
• Mathematics
• 1976
The problem—does every closed Riemannian manifold of dimension greater than one have infinitely many geometrically distinct periodic geodesies—has received much attention. An affirmative answer is
Lefschetz fibrations and symplectic homology
This paper is about the symplectic topology of Stein manifolds. If we have a symplectic manifold .V; !/, then we say it carries a Stein structure if there exists a complex structure J and an
The Künneth formula in Floer homology for manifolds with restricted contact type boundary
We prove the Künneth formula in Floer (co)homology for manifolds with restricted contact type boundary. We use Viterbo's definition of Floer homology, involving the symplectic completion by adding a
A FLOER HOMOLOGY FOR EXACT CONTACT EMBEDDINGS
• Mathematics
• 2007
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