A FLOER HOMOLOGY FOR EXACT CONTACT EMBEDDINGS

By Kai Cieliebak, Urs Frauenfelder. 2007

145 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/93b5b984e648955b67d5feb8ecae1e71b8ba424d

How researchers see this paper

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In Geometry and Topology

1. A. Oancea
2. Alexander F. Ritter
3. Kai Cieliebak
4. Otto van Koert
5. Frederick J. Bourgeois III
6. Urs Frauenfelder
7. P. Seidel
8. M. Abouzaid

In Mathematical Physics

1. A. Oancea
2. Alexander F. Ritter
3. Kai Cieliebak
4. Frederick J. Bourgeois III
5. Otto van Koert
6. Urs Frauenfelder
7. P. Seidel
8. M. Abouzaid

Citations in the corpus

• Contact geometry of the restricted three‐body problem (2010, methodology): “…type we can apply the theorem by Cieliebak-Frauenfelder-Oancea [6] and obtain that the Rabinowitz Floer homology of the energy hypersurface as defined by Cieliebak-Frauenfelder [5] is isomorphic to the direct sum of symplectic homology and cohomology (except possibly in finitely many degrees.)”
• Rabinowitz Floer homology and symplectic homology (2009, methodology): “This argument has already appeared in [9].”
• Symplectic homology and the Eilenberg-Steenrod axioms (2015, methodology): “Given a pair of Liouville domains (W,V ), Rabinowitz-Floer homology RFH∗(∂V,W ) was defined in [27] as a Floer-type theory associated to the Rabinowitz action functional”
• Topological quantum field theory structure on symplectic cohomology (2010, methodology): “If ∂M⊂X is displaceable then RFH∗(∂M⊂X)=0 by Cieliebak-Frauenfelder [11].”
• $S^1$-equivariant symplectic homology and linearized contact homology (2012, methodology): “Yet another remark is that the techniques of this paper can be adapted in order to define S(1)-equivariant Rabinowitz Floer homology (see [20] for the original construction).”
• Leaf-wise intersections and Rabinowitz Floer homology (2008, unknown): “logy. 1 2 PETER ALBERS AND URS FRAUENFELDER If the full Rabinowitz Floer homology is non-zero we obtain much stronger results. For the construction of Rabinowitz Floer homology we refer the reader to [CF09], see also Section 2.3. Theorem C. If the Rabinowitz Floer homology of (M,Σ) does not vanish, ”
• First steps in stable Hamiltonian topology (2010, background): “(This is proved in [11] in the case without boundary; it carries over to the case with boundary provided there are no periodic orbits near the boundary).”