Hui, Wing San. / Thesis submitted in: November 2003. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 58-60). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Outline of Thesis --- p.2 / Chapter 2 --- Basic Knowledge of Knot Theory --- p.3 / Chapter 2.1 --- Preparation --- p.3 / Chapter 2.1.1 --- "Knots, Knot Equivalence and Isotopic Knot" --- p.3 / Chapter 2.1.2 --- Tame and Wild Knots --- p.5 / Chapter 2.2 --- Some Invariants and Quantities about Knot --- p.7 / Chapter 2.2.1 --- Projection of Knot and Crossing Number --- p.7 / Chapter 2.2.2 --- Braids and Braid Index --- p.7 / Chapter 3 --- Minimal Stick Number --- p.11 / Chapter 3.1 --- History and Definition --- p.11 / Chapter 3.2 --- Minimal Stick Number on Some Simple Knots --- p.12 / Chapter 3.3 --- Some Theorems on the Minimal Stick Number --- p.14 / Chapter 4 --- Superbridge Index --- p.22 / Chapter 4.1 --- "Definitions of Bridge Index, Superbridge Index and Total Curvature" --- p.22 / Chapter 4.2 --- Superbridge Index and Braid Index --- p.25 / Chapter 4.3 --- "Relations between Bridge Index, Superbridge Index and Total Curvature" --- p.29 / Chapter 4.4 --- Superbridge Index and Minimal Stick Number --- p.36 / Chapter 5 --- The Geometric Knot Space --- p.37 / Chapter 5.1 --- Definition of the Geometric Knot Space --- p.37 / Chapter 5.2 --- "Geometric Equivalence and Topological Properties of the Geometric Knot Space, Geo(n)" --- p.39 / Chapter 5.3 --- "The Spaces Geo(3), Geo(4) and Geo(5)" --- p.40 / Chapter 5.4 --- Topology of the Space Geo(6) --- p.43 / Chapter 6 --- Concluding Remarks --- p.52 / Chapter 6.1 --- Other Results on the Minimal Stick Number --- p.52 / Chapter 6.2 --- Minimal Stick Number and Superbridge Index of the Torus Knot --- p.54 / Chapter 6.3 --- Explorations of the Geometric Knot Spaces --- p.56 / Bibliography --- p.58
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324782 |
| Date | January 2004 |
| Contributors | Hui, Wing San., 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, iii, 60 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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