Overview

"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 is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds."

Full Product Details

Author:   Dale Rolfsen
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   v. 346
Dimensions:   Width: 26.20cm , Height: 2.80cm , Length: 18.40cm
Weight:   0.945kg
ISBN:  

9780821834367

ISBN 10:   0821834363
Pages:   439
Publication Date:   30 November 2003
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Temporarily unavailable  
The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you.

Table of Contents

Introduction Codimension one and other matters The fundamental group Three-dimensional PL geometry Seifert surfaces Finite cyclic coverings and the torsion invariants Infinite cyclic coverings and the Alexander invariant Matrix invariants 3-manifolds and surgery on links Foliations, branched covers, fibrations and so on A higher-dimensional sampler Covering spaces and some algebra in a nutshell Dehn's lemma and the loop theorem Table of knots and links References Index.

Reviews

…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

...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

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