Ku Wah Kwan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 61-64). / Abstracts in English and Chinese. / Chapter 1 --- Basic 3-Dimensional Contact Geometry --- p.5 / Chapter 1.1 --- Introduction --- p.5 / Chapter 1.2 --- Contact Structure --- p.7 / Chapter 1.3 --- Darboux's Theorem --- p.11 / Chapter 1.4 --- Characteristic Foliation --- p.13 / Chapter 1.5 --- More About S3 with The Standard Contact Structure --- p.16 / Chapter 2 --- Legendrian Knots --- p.18 / Chapter 2.1 --- Basic Definition --- p.18 / Chapter 2.2 --- Front Projection --- p.19 / Chapter 2.3 --- Classical Legendrian Knot Invariants --- p.22 / Chapter 2.3.1 --- Thurston-Bennequin Invariant --- p.22 / Chapter 2.3.2 --- Rotation Number --- p.23 / Chapter 2.4 --- Stabilization --- p.24 / Chapter 3 --- Convex Surface Theory --- p.26 / Chapter 3.1 --- Contact Vector Field --- p.26 / Chapter 3.2 --- Convex Surfaces --- p.29 / Chapter 3.3 --- Flexibility of Characteristic Foliation --- p.34 / Chapter 3.4 --- Bennequin Inequality --- p.36 / Chapter 3.5 --- Bypass --- p.38 / Chapter 3.5.1 --- Modification of Dividing Curves through Bypass --- p.39 / Chapter 3.5.2 --- Relation of Bypass and Stabilizing Disk --- p.40 / Chapter 3.5.3 --- Finding Bypass --- p.40 / Chapter 3.6 --- Tight Contact Structures on Solid Tori --- p.41 / Chapter 4 --- Classification Results --- p.42 / Chapter 4.1 --- Unknot --- p.43 / Chapter 4.2 --- Positive Torus Knot --- p.45 / Chapter 5 --- Transverse Knots --- p.50 / Chapter 5.1 --- Basic Definition --- p.50 / Chapter 5.2 --- Self-linking Number --- p.54 / Chapter 5.3 --- Relation between Transverse Knot and Legendrian Knot --- p.55 / Chapter 5.4 --- Classification of Unknot and Torus Knot --- p.57 / Chapter 6 --- Recent Development --- p.60 / Bibliography --- p.61
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324752 |
| Date | January 2004 |
| Contributors | Ku, Wah Kwan., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 64 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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