Topics on thickness and ropelength.

• Other Authors: Liu, Chun-Lung.
• Format: Others
• Language: English
• Published: 2006
• Subjects: Knot theory
• Online Access: http://library.cuhk.edu.hk/record=b5892854; http://repository.lib.cuhk.edu.hk/en/item/cuhk-325491

Liu Chun-Lung. === Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. === Includes bibliographical references (leaves 98-100). === Chapter 1 --- Introduction --- p.5 === Chapter 2 --- Fundamentals of thickness --- p.7 === Chapter 2.1 --- Definition of thickness --- p.9 === Chapter 2.2 --- Basic theorem and corollaries --- p.10 === Chapter 2.3 --- Equivalent definitions --- p.17 === Chapter 3 --- Ropelength minimizer --- p.19 === Chapter 3.1 --- Existence of ropelength minimizer --- p.20 === Chapter 3.2 --- Some ropelength minimizers --- p.23 === Chapter 4 --- Thickness computation --- p.27 === Chapter 4.1 --- Definitions --- p.28 === Chapter 4.2 --- Octrope algorithm --- p.33 === Chapter 4.3 --- Minor improvements --- p.45 === Chapter 5 --- Arc presentation --- p.54 === Chapter 5.1 --- Definitions --- p.55 === Chapter 5.2 --- Basic Theorems --- p.57 === Chapter 5.3 --- Ropelength upper bound --- p.64 === Chapter 6 --- Hamiltonian knot projection --- p.74 === Chapter 6.1 --- Hamiltonian RPG --- p.75 === Chapter 6.2 --- Embedding of RPG --- p.78 === Chapter 6.3 --- Ropelength upper bound --- p.95 === Bibliography --- p.98