AMS Chelsea Publishing
Volume: 346;
1976;
439 pp;
Hardcover
MSC: Primary 57;
Print ISBN: 978-0-8218-3436-7
Product Code: CHEL/346.H
List Price: $61.00
AMS Member Price: $54.90
MAA Member Price: $54.90
Electronic ISBN: 978-1-4704-2997-3
Product Code: CHEL/346.H.E
List Price: $61.00
AMS Member Price: $54.90
MAA Member Price: $54.90
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Supplemental Materials
Knots and Links
Share this pageDale Rolfsen
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
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.
Readership
Advanced undergraduates, graduate students, and research mathematicians interested in knot theory and its applications to low-dimensional topology.
Reviews & Endorsements
...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
Table of Contents
Table of Contents
Knots and Links
- Cover Cover11
- Frontispiece ii3
- Title page iii4
- Dedication v6
- Preface to the AMS Chelsea edition vii8
- Preface to the second printing ix10
- Preface xi12
- Contents xiii14
- Introduction 118
- Codimension one and other matters 825
- The fundamental group 4764
- Three-dimensional PL geometry 100117
- Seifert surfaces 118135
- Finite cyclic coverings and the torsion invariants 145162
- Infinite cyclic coverings and the Alexander invariant 160177
- Matrix invariants 200217
- 3-manifolds and surgery on links 233250
- Foliations, branched covers, fibrations and so on 284301
- A higher-dimensional sampler 342359
- Appendix A. Covering spaces and some algebra in a nutshell 358375
- Appendix B. Dehn’s lemma and the loop theorem 374391
- Appendix C. Table of knots and links 388405
- References 430447
- Index 438455
- Back Cover Back Cover1458