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

part I|6 pages

Introduction and History of Knots

part II|76 pages

Standard and Nonstandard Representations of Knots

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 XIV|68 pages

Physical Knot Theory

part XV|28 pages

Knots and Science