Topics on thickness and ropelength.

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