Cioba, Alexandru;
(2018)
Nicely embedded curves in symplectic cobordisms.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
In the following text we investigate the properties of moduli spaces of so-called “nicely embedded” curves in Liouville symplectic cobordisms. We exhibit a topological obstruction which occurs in contact manifolds cobordant to the tight 3- sphere, namely the presence of an unknotted Reeb orbit, with self-linking number 1. The same result is shown to apply in overtwisted manifolds. A similar proof establishes the result in reducible contact manifolds. Along the way we recall several classical results, and prove a series of auxiliary lemmas. Throughout most of the work we limit ourselves to the context of 4-dimensional cobordisms, where intersection theory for pseudoholomorphic curves is an indispensable tool.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Nicely embedded curves in symplectic cobordisms |
| Event: | UCL (University College London) |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| UCL classification: | UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10054430 |
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