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LinKnot: Knot Theory by Computer

Slavik Jablan and Radmila Sazdanović
World Scientific
Publication Date: 
Number of Pages: 
Series on Knots and Everything 21
[Reviewed by
Charles Ashbacher
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This book is written for the dedicated knot theorist willing to use the LinKnot add-on to Mathematica. The first chapter presents the basic notation of knots and links and is relatively easy to follow if you have any exposure to knot theory. As long as you are familiar with the representations such as the Conway notation, classification schema and invariants then you could most likely skip this chapter.

Chapter two is the heavy portion of the book; it is heavily populated with tables listing the classification parameters and generators of knots and links. Unless you are an expert in the field, this is very slow reading if your goal is complete understanding. Fortunately, diagrams are frequently used to clarify the classifications. For example, on pages 244 and 245, there are figures of the basic polyhedra with less than 11 crossings and those with exactly 12 crossings. Like all the other diagrams, these are very well done. All the diagrams are all easy to understand, even when they are at their most complex level.

The third and final chapter is a history of knot theory and some applications of knots and links. The two main sections of applications, with several subsections, are mirror curves and KLs and fullerenes. Three short sections called: KLs and logic, waveforms, and knot automata complete the book.

With the advantage of computer software designed to classify all knots satisfying specific properties, it is possible to easily list them. Which is what the authors do. If that is your interest, then all of this book will interest you. Absent that, there will be many classification sections that you will skip by pushing the “I believe” button.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

  • Notation of Knots and Links
  • Recognition and Generation of Knots and Links
  • History of Knot Theory and Applications of Knots and Links