ABSTRACT
"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject."
– Ed Witten, Recipient of the Fields Medal
"I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field."
– Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis
Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers.
Features
- Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers
- Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees
- Edited and contributed by top researchers in the field of knot theory
TABLE OF CONTENTS
part I|6 pages
Introduction and History of Knots
part II|76 pages
Standard and Nonstandard Representations of Knots
part III|20 pages
Tangles
part IV|82 pages
Types of Knots
part V|36 pages
Knots and Surfaces
part VI|38 pages
Invariants Defined in Terms of Min and Max
part VII|152 pages
Other Knotlike Objects
part VIII|48 pages
Higher Dimensional Knot Theory
part IX|70 pages
Spatial Graph Theory
part X|72 pages
Quantum Link Invariants
part XI|66 pages
Polynomial Invariants
part XII|96 pages
Homological Invariants
part XIII|68 pages
Algebraic and Combinatorial Invariants
part XIV|68 pages
Physical Knot Theory
part XV|28 pages
Knots and Science