Jorge Alberto Calvo

Kenneth C. Millett

David M Goldschmidt

AMS Special Session on Physical Knotting

Eric J. Rawdon

Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in April 2001, this volume discusses critical questions and new ideas in the areas of knotting and folding of curves in surfaces in three-dimensional space and applications of these ideas to biology, chemistry, computer science, and engineering. 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.

Knotting, Linking, and Folding Geometric Objects in R3 : AMS Special Session on Physical Knotting and Unknotting, Las Vegas, Nevada, April 21-22, 2001

Physical Knots

Proceedings of a Symposium held at Santa Barbara in honor of Raymond L. Wilder, July 25 - 29, 1977

Algebraic and Geometric Topology

Louis H. Kauffman

Sofia Lambropoulou

Colin C. Adams

Cameron McA. Gordon

Vaughan F.R. Jones

Jozef H. Przytycki

Renzo Ricca

Radmila Sazdanovic

This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.

Knots in Hellas, International Olympic Academy, Greece, July 2016

Knots, Low-Dimensional Topology and Applications

Kenneth C. Millett

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