Rabinowitz Floer homology and symplectic homology  [ Homologie de Rabinowitz-Floer et homologie symplectique ]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 43 (2010) no. 6, p. 957-1015
Étant donné un plongement exact et séparant d’une variété de contact (M,ξ) dans une variété symplectique (W,ω), les deux premiers auteurs ont défini des groupes d’homologie dits de Rabinowitz Floer RFH * (M,W). Ceux-ci dépendent uniquement de la composante bornée V de WM. Nous construisons une suite exacte longue dans laquelle la cohomologie symplectique de V est envoyée vers l’homologie symplectique de V, qui à son tour est envoyée vers l’homologie de Rabinowitz Floer RFH * (M,W), qui finalement est envoyée vers la cohomologie symplectique de V. Nous calculons RFH * (ST * L,T * L) pour le fibré cotangent unitaire ST * L d’une variété compacte sans bord L. Nous démontrons que l’image d’un plongement exact et séparant de ST * L ne peut pas être disjointe d’elle-même par une isotopie hamiltonienne, à condition que le plongement induise une injection sur le groupe fondamental et dimL4.
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,ξ) into a symplectic manifold (W,ω). These depend only on the bounded component V of WM. 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 dimL4 and the embedding induces an injection on π 1 .
DOI : https://doi.org/10.24033/asens.2137
Classification:  53D35,  53D40
Mots clés: homologie symplectique, homologie de Rabinowitz Floer, plongements de contact, espaces de lacets libres
@article{ASENS_2010_4_43_6_957_0,
     author = {Cieliebak, Kai and Frauenfelder, Urs and Oancea, Alexandru},
     title = {Rabinowitz Floer homology and symplectic homology},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 43},
     number = {6},
     year = {2010},
     pages = {957-1015},
     doi = {10.24033/asens.2137},
     zbl = {1213.53105},
     mrnumber = {2778453},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2010_4_43_6_957_0}
}
Cieliebak, Kai; Frauenfelder, Urs; Oancea, Alexandru. Rabinowitz Floer homology and symplectic homology. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 43 (2010) no. 6, pp. 957-1015. doi : 10.24033/asens.2137. http://www.numdam.org/item/ASENS_2010_4_43_6_957_0/

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