On Knots. (AM-115) [Paperback]

Louis H. Kauffman (Author)

Editorial Reviews

Review

On Knots is chatty, and very pleasant for browsing. There are lots of wonderful illustrations and a wealth of detail from the author's bag of tricks, gathered over the years, relating to the combinatorics of knot diagrams and also to Seifert pairings, cobordism, signature invariants (several different ones), the Arf invariant, and the ubiquitous Alexander polynomial. There are many challenges to the reader to explore combinatorial patterns, which makes the book stimulating. -- American Mathematical Society

Product Details

• Paperback: 498 pages
• Publisher: Princeton University Press (October 1, 1987)
• Language: English
• ISBN-10: 0691084351
• ISBN-13: 978-0691084350
• Product Dimensions: 9.2 x 5.9 x 1.4 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,968,109 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

7 of 7 people found the following review helpful:

4.0 out of 5 stars A good reference/second book on knot theory, May 27, 2001

By 

Ollie Nanyes (Peoria, IL USA) - See all my reviews
(REAL NAME)   

This review is from: On Knots. (AM-115) (Paperback)

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.

3 of 5 people found the following review helpful:

4.0 out of 5 stars Good intro to knot theory, with a lot of technical detail, January 9, 1999

By A Customer

This review is from: On Knots. (AM-115) (Paperback)

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.