Étant donné un plongement exact et séparant d’une variété de contact dans une variété symplectique , les deux premiers auteurs ont défini des groupes d’homologie dits de Rabinowitz Floer . Ceux-ci dépendent uniquement de la composante bornée de . Nous construisons une suite exacte longue dans laquelle la cohomologie symplectique de est envoyée vers l’homologie symplectique de , qui à son tour est envoyée vers l’homologie de Rabinowitz Floer , qui finalement est envoyée vers la cohomologie symplectique de . Nous calculons pour le fibré cotangent unitaire d’une variété compacte sans bord . Nous démontrons que l’image d’un plongement exact et séparant de 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 .
The first two authors have recently defined Rabinowitz Floer homology groups associated to a separating exact embedding of a contact manifold into a symplectic manifold . These depend only on the bounded component of . We construct a long exact sequence in which symplectic cohomology of maps to symplectic homology of , which in turn maps to Rabinowitz Floer homology , which then maps to symplectic cohomology of . We compute , where is the unit cosphere bundle of a closed manifold . As an application, we prove that the image of a separating exact contact embedding of cannot be displaced away from itself by a Hamiltonian isotopy, provided and the embedding induces an injection on .
@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}, volume = {43}, year = {2010}, pages = {957-1015}, doi = {10.24033/asens.2137}, mrnumber = {2778453}, zbl = {1213.53105}, language = {en}, url = {http://dml.mathdoc.fr/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, Tome 43 (2010) pp. 957-1015. doi : 10.24033/asens.2137. http://gdmltest.u-ga.fr/item/ASENS_2010_4_43_6_957_0/
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