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H 1 Existence of Liouville structures on cobordisms

Auteurs : Murphy, Emmy (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Given a smooth cobordism with an almost complex structure, one can ask whether it is realized as a Liouville cobordism, that is, an exact symplectic manifold whose primitive induces a contact structure on the boundary. We show that this is always the case, as long as the positive and negative boundaries are both nonempty. The contact structure on the negative boundary will always be overtwisted in this construction, but for dimensions larger than 4 we show that the positive boundary can be chosen to have any given contact structure. In dimension 4 we show that this cannot always be the case, due to obstructions from gauge theory.

    Codes MSC :
    53D05 - Symplectic manifolds
    53D10 - Contact manifolds, general
    53D35 - Global theory of symplectic and contact manifolds

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 17/06/15
      Date de captation : 02/06/15
      Collection : Research talks ; Geometry ; Topology
      Format : quicktime ; audio/x-aac
      Durée : 01:05:10
      Domaine : Topology ; Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-06-02_Murphy.mp4

    Informations sur la rencontre

    Nom de la rencontre : Jean-Morlet Chair: Moduli spaces in symplectic topology and in Gauge theory / Chaire Jean-Morlet : Espaces de modules en topologie symplectique et en théorie de Jauge
    Organisateurs de la rencontre : Hofer, Helmut ; Itenberg, Ilia ; Lalonde, François ; McDuff, Dusa ; Ono, Kaoru ; Polterovich, Leonid ; Teleman, Andrei
    Dates : 01/06/15 - 05/06/15
    Année de la rencontre : 2015
    URL Congrès : http://lalondeteleman.weebly.com/main-co...

    Citation Data

    DOI : 10.24350/CIRM.V.18770203
    Cite this video as: Murphy, Emmy (2015). Existence of Liouville structures on cobordisms. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18770203
    URI : http://dx.doi.org/10.24350/CIRM.V.18770203


    Bibliographie

    1. Eliashberg, Y., & Murphy, E. (2015). Making cobordisms symplectic. - http://arxiv.org/abs/1504.06312

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