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Nicely embedded curves in symplectic cobordisms

Cioba, Alexandru; (2018) Nicely embedded curves in symplectic cobordisms. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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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: http://discovery.ucl.ac.uk/id/eprint/10054430
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