Hardcover ISBN:  9780821834367 
Product Code:  CHEL/346.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470429973 
Product Code:  CHEL/346.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9780821834367 
eBook: ISBN:  9781470429973 
Product Code:  CHEL/346.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 
Hardcover ISBN:  9780821834367 
Product Code:  CHEL/346.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470429973 
Product Code:  CHEL/346.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9780821834367 
eBook ISBN:  9781470429973 
Product Code:  CHEL/346.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 

Book DetailsAMS Chelsea PublishingVolume: 346; 1976; 439 ppMSC: Primary 57
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 threemanifolds.
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 threemanifolds; and visualize knots and their complements. It is characterized by its handson 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 3manifolds.
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.
ReadershipAdvanced undergraduates, graduate students, and research mathematicians interested in knot theory and its applications to lowdimensional topology.

Table of Contents

Chapters

Chapter 1. Introduction

Chapter 2. Codimension one and other matters

Chapter 3. The fundamental group

Chapter 4. Threedimensional PL geometry

Chapter 5. Seifert surfaces

Chapter 6. Finite cyclic coverings and the torsion invariants

Chapter 7. Infinite cyclic coverings and the Alexander invariant

Chapter 8. Matrix invariants

Chapter 9. 3manifolds and surgery on links

Chapter 10. Foliations, branched covers, fibrations and so on

Chapter 11. A higherdimensional sampler

Appendix A. Covering spaces and some algebra in a nutshell

Appendix B. Dehn’s lemma and the loop theorem

Appendix C. Table of knots and links


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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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 threemanifolds.
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 threemanifolds; and visualize knots and their complements. It is characterized by its handson 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 3manifolds.
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.
Advanced undergraduates, graduate students, and research mathematicians interested in knot theory and its applications to lowdimensional topology.

Chapters

Chapter 1. Introduction

Chapter 2. Codimension one and other matters

Chapter 3. The fundamental group

Chapter 4. Threedimensional PL geometry

Chapter 5. Seifert surfaces

Chapter 6. Finite cyclic coverings and the torsion invariants

Chapter 7. Infinite cyclic coverings and the Alexander invariant

Chapter 8. Matrix invariants

Chapter 9. 3manifolds and surgery on links

Chapter 10. Foliations, branched covers, fibrations and so on

Chapter 11. A higherdimensional sampler

Appendix A. Covering spaces and some algebra in a nutshell

Appendix B. Dehn’s lemma and the loop theorem

Appendix C. Table of knots and links

...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