In this thesis, we define a new invariant of a Legendrian knot in a contact manifold using an open book decomposition supporting the contact structure. We define the support genus of a Legendrian knot L in a contact 3-manifold as the minimal genus of a page of an open book of M supporting the contact structure such that L sits on a page and the framings given by the contact structure and the page agree. For any topological link in 3-sphere we construct a planar open book decomposition whose monodromy is a product of positive Dehn twists such
that the planar open book contains the link on its page. Using this, we show any topological link, in particular any knot in any 3-manifold M sits on a page of a planar open book decomposition of M and we show any null-homologous loose
Legendrian knot in an overtwisted contact structure has support genus zero.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/2/12610791/index.pdf |
| Date | 01 July 2009 |
| Creators | Celik Onaran, Sinem |
| Contributors | Celik Onaran, Sinem |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for METU campus |
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