The properties of knotted and linked configurations in space have long been of interest to physicists and mathematicians. More recently and more widely, they have become important to biologists, chemists, computer scientists, and engineers. The depth and breadth of their applications are widely appreciated. Nevertheless, fundamental and challenging questions remain to be answered.

Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in April 2001, this volume discusses critical questions and introduces new ideas that will stimulate multi-disciplinary applications.

Some of the papers are primarily theoretical; others are experimental. Some are purely mathematical; others deal with applications of mathematics to theoretical computer science, engineering, physics, biology, or chemistry. Connections are made between classical knot theory and the physical world of macromolecules, such as DNA, geometric linkages, rope, and even cooked spaghetti.

This book introduces the world of physical knot theory in all its manifestations and points the way for new research. It is suitable for a diverse audience of mathematicians, computer scientists, engineers, biologists, chemists, and physicists.

Readership

Graduate students, mathematicians, computer scientists, engineers, biologists, chemists, and physicists.

Table of Contents

• J. Simon -- Physical knots
• R. Randell -- The space of piecewise-linear knots
• J. A. Calvo -- Characterizing polygons in \(\mathbb{R}^3\)
• E. J. Rawdon and R. G. Scharein -- Upper bounds for equilateral stick numbers
• K. C. Millett -- An investigation of equilateral knot spaces and ideal physical knot configurations
• T. Deguchi and M. K. Shimamura -- Topological effects on the average size of random knots
• A. Dobay, P.-E. Sottas, J. Dubochet, and A. Stasiak -- Bringing an order into random knots
• E. J. J. van Rensburg -- The probability of knotting in lattice polygons
• E. J. J. van Rensburg -- Knotting in adsorbing lattice polygons
• P. Pieranski and S. Przybyl -- In search of the ideal trefoil knot
• Y. Diao and C. Ernst -- The crossing numbers of thick knots and links
• R. Kusner -- On thickness and packing density for knots and links
• J. M. Sullivan -- Approximating ropelength by energy functions
• R. Langevin and J. O'Hara -- Conformal geometric viewpoints for knots and links I
• O. Gonzalez, J. H. Maddocks, and J. Smutny -- Curves, circles, and spheres
• G. Dietler, P. Pieranski, S. Kasas, and A. Stasiak -- The rupture of knotted strings under tension
• L. H. Kauffman and S. Lambropoulou -- Classifying and applying rational knots and rational tangles
• D. Roseman -- Untangling some spheres in \(\mathbb{R}^4\) by energy minimizing flow
• M. Soss and G. T. Toussaint -- Convexifying polygons in 3D: A survey
• R. Connelly, E. D. Demaine, and G. Rote -- Infinitesimally locked self-touching linkages with applications to locked trees
• L. H. Kauffman -- Biologic