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

Collection 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

Organizer(s) Hofer, Helmut ; Itenberg, Ilia ; Lalonde, François ; McDuff, Dusa ; Ono, Kaoru ; Polterovich, Leonid ; Teleman, Andrei
Date(s) 01/06/2015 - 05/06/2015
linked URL https://www.chairejeanmorlet.com/1256.html
00:00:00 / 00:00:00
3 6

Existence of Liouville structures on cobordisms

By Emmy Murphy

Also appears in collections : Distinguished women in mathematics, Exposés de recherche

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.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.18770203
  • Cite this video Murphy, Emmy (02/06/2015). Existence of Liouville structures on cobordisms. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18770203
  • URL https://dx.doi.org/10.24350/CIRM.V.18770203

Bibliography

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback