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Editorial Reviews
Product 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.
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.
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Inside This Book
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First Sentence:
The possibility of a mathematical study of knots was probably recognized first by C. F. Gauss. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
standard ball pair, fibred knot, unknotting theorem, slice knot, tame knot, surgery coefficients, boundary connected sum, surgery manifold, infinite cyclic cover, open book decomposition, link pictured, branched cyclic cover, surgery instructions, closed connected orientable, solid tori, ambient isotopy, knot group, preferred longitude, torsion numbers, torsion invariants, branched cover, surgery description, ambient isotopic, presentation matrix, solid torus Key Phrases - Capitalized Phrases (CAPs): (learn more)
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The possibility of a mathematical study of knots was probably recognized first by C. F. Gauss. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
standard ball pair, fibred knot, unknotting theorem, slice knot, tame knot, surgery coefficients, boundary connected sum, surgery manifold, infinite cyclic cover, open book decomposition, link pictured, branched cyclic cover, surgery instructions, closed connected orientable, solid tori, ambient isotopy, knot group, preferred longitude, torsion numbers, torsion invariants, branched cover, surgery description, ambient isotopic, presentation matrix, solid torus Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fox's Quick Trip New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 5
books:
99
books
cite this book:
See all 99 books citing this book
- Lectures on algebraic topology (Mathematics lecture note series) by Marvin J Greenberg in Back Matter
- Analytic Function Theory, Volume I (AMS Chelsea Publishing) by Einar Hille in Back Matter
- The Theory of Groups by Hans J. Zassenhaus on page 205
- Algebraic Topology: A First Course (Mathematics Lecture Note Series) by Marvin J. Greenberg in Back Matter
- Dimension Theory (Princeton Mathematical Ser.; Vol 4) by Witold Hurewicz on page 33
- Knots '90: Proceedings of the International Conference on Knot Theory and Related Topics Held in Osaka (Japan, August 15-19, 1990) by Akio Kawauchi on 5 pages
- The Mystery of Knots: Computer Programming for Knot Tabulation (Series on Knots and Everything, Volume 20) by Charilaos Aneziris on 4 pages
- Braid Group, Knot Theory and Statistical Mechanics II (Advanced Series in Mathematical Physics, Vol 17) (v. 2) by C. N. Yang on page 57, page 232, and page 293
- History and Science of Knots (Series on Knots and Everything , Vol 11) by J. C. Turner on page 254, page 258, and page 295
- Real Mathematical Analysis by Charles Chapman Pugh on page 108, page 134, and page 416
See all 99 books citing this book
Books on Related Topics
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What Do Customers Ultimately Buy After Viewing This Item?
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72% buy the item featured on this page: Knots and Links (AMS Chelsea Publishing)$39.15 |
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12% buy The Knot Book $29.40 |
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10% buy Formal Knot Theory (Dover Books on Mathematics) $11.66 |
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6% buy 3-Manifolds (AMS Chelsea Publishing) $29.40 |
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