On Knots. (AM-115)
By Louis H. Kauffman
- Publisher: Princeton University Press
- Number Of Pages: 498
- Publication Date: 1987-10-01
- ISBN-10 / ASIN: 0691084351
- ISBN-13 / EAN: 9780691084350
- Binding: Paperback
Summary: A good reference/second book on knot theory
I don't feel that this book would be the best systematic introduction to the subject (say, for a course on knot theory). However, once someone has been introduced to knot theory(say, via a topology of manifolds class, more elementary book such as Adams, Livingston, or even a more advanced book such as Zieshang-Burde, Lickorish or Rolfsen), this book is an excellent reference.
The strength of this book is the "hands on" explinations given about many of the standard topics on knot theory (Alexander polynomial, Skein invariants, covering spaces, etc.) and I feel that the author does a great job on relating many of the combinatorial invariants to the topology of the knot complement. Many informative illustrations and examples are provided. This is one of the first references I look to when I need a refresher on a topic, or if I encounter something in classical knot theory that I am unfamiliar with.
Also, this book is just plain fun to read!
Of course, this book is from the mid 80's and therefore does not cover some of the more modern material.
Frankly, I've found that anything written by professor Kauffman to be well written and worth reading.
Summary: Good intro to knot theory, with a lot of technical detail
Starting out with the basics, Kauffman moves on quickly to more difficult concepts using advanced math. The book has a great section on knot tricks, and a nice table of knots.