Knots and Links (AMS Chelsea Publishing) by Dale Rolfsen (PDF)

Description

Rolfsen’s beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen’s theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers ‘practical’ training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are “”The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes”” and “”The Knot Book””.

User’s Reviews

Editorial Reviews: Review …a gem and a classic. Every mathematics library should own a copy and every mathematician should read at least some of it. The writing is clear and engaging, while the choice of examples is genius…Rolfsen’s book continues to be a beautiful introduction to some beautiful ideas. –Scott A. Taylor, MAA Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This classic introduction to knot theory has not faded with time and, to my surprise, its 2003 AMS corrected reprint still lists 166 prime knots with 10 crossing (noting, as in the 1990 edition, that two of them are equivalent). It seems that the author, to his credit, has not adopted the confusing renumbering of four of them. Still missing, however, is any reference to my 1974 AMS Proceedings paper, which identified the error in the book’s 1976 first edition.

⭐Took more than a month to get the book. But the book is great! Packed well and brand new! Exactly the same edition as the picture.

⭐I’m not a knot theorist or topologist at all, but I’ve found this useful as a source for basic results and for picking up some basic facts about knots and low-dimensional topology. It’s widely cited, and for good reasons.Missing many important recent (and even not-so-recent by now) topics, but perhaps this is not the right place for them anyway.

⭐great book!!

⭐excellent edition of this knot theory classicbeautifully illustratedrecommended

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