Existence of Liouville structures on cobordisms | Vidéo | Carmin.tv

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Existence of Liouville structures on cobordisms

Appears in collections : 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, 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

Date of recording 02/06/2015
Date of publication 17/06/2015
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

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

Domain(s)

Bibliography

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

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