Applications of Knot Theory
About this Title
Dorothy Buck, Imperial College London, London, England and Erica Flapan, Pomona College, Claremont, CA, Editors
Publication: Proceedings of Symposia in Applied Mathematics
Publication Year: 2009; Volume 66
ISBNs: 978-0-8218-4466-3 (print); 978-0-8218-9281-7 (online)
Over the past 20–30 years, knot theory has rekindled its historic ties with biology, chemistry, and physics as a means of creating more sophisticated descriptions of the entanglements and properties of natural phenomena—from strings to organic compounds to DNA.
This volume is based on the 2008 AMS Short Course, Applications of Knot Theory. The aim of the Short Course and this volume, while not covering all aspects of applied knot theory, is to provide the reader with a mathematical appetizer, in order to stimulate the mathematical appetite for further study of this exciting field.
No prior knowledge of topology, biology, chemistry, or physics is assumed. In particular, the first three chapters of this volume introduce the reader to knot theory (by Colin Adams), topological chirality and molecular symmetry (by Erica Flapan), and DNA topology (by Dorothy Buck). The second half of this volume is focused on three particular applications of knot theory. Louis Kauffman discusses applications of knot theory to physics, Nadrian Seeman discusses how topology is used in DNA nanotechnology, and Jonathan Simon discusses the statistical and energetic properties of knots and their relation to molecular biology.
Graduate students and research mathematicians interested in knot theory and applications.
Table of Contents
- Colin Adams – A brief introduction to knot theory from the physical point of view [MR 2508726]
- Erica Flapan – Topological chirality and symmetries of non-rigid molecules [MR 2508727]
- Dorothy Buck – DNA topology [MR 2508728]
- Louis H. Kauffman – Knots and physics [MR 2508729]
- Nadrian C. Seeman – Synthetic single-stranded DNA topology [MR 2508730]
- Jonathan Simon – Long tangled filaments [MR 2508731]