# Rabinowitz Floer homology and symplectic homology

Kai Cieliebak; Urs Frauenfelder; Alexandru Oancea

Annales scientifiques de l'École Normale Supérieure (2010)

- Volume: 43, Issue: 6, page 957-1015
- ISSN: 0012-9593

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topCieliebak, Kai, Frauenfelder, Urs, and Oancea, Alexandru. "Rabinowitz Floer homology and symplectic homology." Annales scientifiques de l'École Normale Supérieure 43.6 (2010): 957-1015. <http://eudml.org/doc/272182>.

@article{Cieliebak2010,

abstract = {The first two authors have recently defined Rabinowitz Floer homology groups $RFH_*(M,W)$ associated to a separating exact embedding of a contact manifold $(M,\xi )$ into a symplectic manifold $(W,\omega )$. These 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 unit cosphere bundle of a closed manifold $L$. As an application, we prove that the image of a separating exact contact embedding of $ST^*L$ cannot be displaced away from itself by a Hamiltonian isotopy, provided $\dim \,L\ge 4$ and the embedding induces an injection on $\pi _1$.},

author = {Cieliebak, Kai, Frauenfelder, Urs, Oancea, Alexandru},

journal = {Annales scientifiques de l'École Normale Supérieure},

keywords = {symplectic homology; Rabinowitz Floer homology; contact embeddings; free loop space},

language = {eng},

number = {6},

pages = {957-1015},

publisher = {Société mathématique de France},

title = {Rabinowitz Floer homology and symplectic homology},

url = {http://eudml.org/doc/272182},

volume = {43},

year = {2010},

}

TY - JOUR

AU - Cieliebak, Kai

AU - Frauenfelder, Urs

AU - Oancea, Alexandru

TI - Rabinowitz Floer homology and symplectic homology

JO - Annales scientifiques de l'École Normale Supérieure

PY - 2010

PB - Société mathématique de France

VL - 43

IS - 6

SP - 957

EP - 1015

AB - The first two authors have recently defined Rabinowitz Floer homology groups $RFH_*(M,W)$ associated to a separating exact embedding of a contact manifold $(M,\xi )$ into a symplectic manifold $(W,\omega )$. These 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 unit cosphere bundle of a closed manifold $L$. As an application, we prove that the image of a separating exact contact embedding of $ST^*L$ cannot be displaced away from itself by a Hamiltonian isotopy, provided $\dim \,L\ge 4$ and the embedding induces an injection on $\pi _1$.

LA - eng

KW - symplectic homology; Rabinowitz Floer homology; contact embeddings; free loop space

UR - http://eudml.org/doc/272182

ER -

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