Geometric knot theory.

• Other Authors: Hui, Wing San.
• Format: Others
• Language: English; Chinese
• Published: 2004
• Subjects: Knot theory
• Online Access: http://library.cuhk.edu.hk/record=b5892032; http://repository.lib.cuhk.edu.hk/en/item/cuhk-324782

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