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# Documents  53D35 | enregistrements trouvés : 2

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## Post-edited  Virtual fundamental cycles and contact homology Pardon, John (Auteur de la Conférence) | CIRM (Editeur )

I will discuss work in progress aimed towards defining contact homology using "virtual" holomorphic curve counting techniques.

## Multi angle  Existence of Liouville structures on cobordisms Murphy, Emmy (Auteur de la Conférence) | CIRM (Editeur )

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. 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 ...

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