L'objet de cet article est de donner une description du groupe fondamental d'une variété symplectique en terme d'objets de la théorie de Floer. À titre d'application, on montre que tous les difféomorphismes hamiltoniens non dégénérés ont, si on les compte avec une notion convenable de multiplicité, suffisamment de points fixes pour engendrer le groupe fondamental.
The main purpose of this paper is to provide a description of the fundamental group of a symplectic manifold in terms of Floer theoretic objects. As an application, we show that when counted with a suitable notion of multiplicity, non degenerate Hamiltonian diffeomorphisms have enough fixed points to generate the fundamental group.
DOI : 10.24033/asens.2366
Keywords: Symplectic topology, Fundamental group, Floer theory, Morse theory, Homotopy, Arnold conjecture.
Mot clés : Topologie symplectique, groupe fondamental, théorie de Floer, théorie de Morse, homotopie, conjecture d'Arnold.
@article{ASENS_2018__51_3_773_0, author = {Barraud, Jean-Fran\c{c}ois}, title = {A {Floer} {Fundamental} group}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {773--809}, publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es}, volume = {Ser. 4, 51}, number = {3}, year = {2018}, doi = {10.24033/asens.2366}, mrnumber = {3831037}, zbl = {1398.57036}, language = {en}, url = {http://www.numdam.org/articles/10.24033/asens.2366/} }
TY - JOUR AU - Barraud, Jean-François TI - A Floer Fundamental group JO - Annales scientifiques de l'École Normale Supérieure PY - 2018 SP - 773 EP - 809 VL - 51 IS - 3 PB - Société Mathématique de France. Tous droits réservés UR - http://www.numdam.org/articles/10.24033/asens.2366/ DO - 10.24033/asens.2366 LA - en ID - ASENS_2018__51_3_773_0 ER -
%0 Journal Article %A Barraud, Jean-François %T A Floer Fundamental group %J Annales scientifiques de l'École Normale Supérieure %D 2018 %P 773-809 %V 51 %N 3 %I Société Mathématique de France. Tous droits réservés %U http://www.numdam.org/articles/10.24033/asens.2366/ %R 10.24033/asens.2366 %G en %F ASENS_2018__51_3_773_0
Barraud, Jean-François. A Floer Fundamental group. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 51 (2018) no. 3, pp. 773-809. doi : 10.24033/asens.2366. http://www.numdam.org/articles/10.24033/asens.2366/
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