The physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year.This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration of spaces of knots, knotted umbilical cords, studies of knots in DNA and proteins, and the structure of tight knots. Together, the chapters explore four major themes: physical knot theory, knot theory in the life sciences, computational knot theory, and geometric knot theory.
Physical Knot Theory: Universal Energy Spectrum of Tight Knots and Links in Physics (R Buniy & T Kephart); Three Knotty Ideas in Geometry: Pearl-Number, Ropelength and Rope Packing (R Kusner & W Kusner); A Tutorial on Knot Energies (E J J van Rensburg); Knot Theory in the Life Sciences: Folding Complexity in a Random-Walk Copolymer Model (G Arteca); Protein Folds, Knots and Tangles (W Taylor); Monte Carlo Simulations of Gel-Electrophoresis of DNA Knots (C Weber et al.); Computational Knot Theory: Ropelength of Tight Polygonal Knots (J Baranska et al.); Topological Entropic Force Between a Pair of Random Knots Forming a Fixed Link (T Deguchi); Universal Characteristics of Polygonal Knot Probabilities (K Millett & E Rawdon); Geometric Knot Theory: Quadrisecants of Knots with Small Crossing Number (G T Jin); Minimal Flat Knotted Ribbons (L Kauffman); Conjectures on the Enumeration of Alternating Links (P Zinn-Justin); and other papers.