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 .
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 .
Keywords: symplectic homology, Rabinowitz Floer homology, contact embeddings, free loop space
Mot 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}, pages = {957--1015}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 43}, number = {6}, year = {2010}, doi = {10.24033/asens.2137}, mrnumber = {2778453}, zbl = {1213.53105}, language = {en}, url = {http://www.numdam.org/articles/10.24033/asens.2137/} }
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 SP - 957 EP - 1015 VL - 43 IS - 6 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/asens.2137/ DO - 10.24033/asens.2137 LA - en ID - ASENS_2010_4_43_6_957_0 ER -
%0 Journal Article %A Cieliebak, Kai %A Frauenfelder, Urs %A Oancea, Alexandru %T Rabinowitz Floer homology and symplectic homology %J Annales scientifiques de l'École Normale Supérieure %D 2010 %P 957-1015 %V 43 %N 6 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/asens.2137/ %R 10.24033/asens.2137 %G en %F 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, Serie 4, Volume 43 (2010) no. 6, pp. 957-1015. doi : 10.24033/asens.2137. http://www.numdam.org/articles/10.24033/asens.2137/
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