
Encyclopedia of Knot Theory
By: Colin Adams (Editor), Erica Flapan (Editor), Allison Henrich (Editor), Louis H. Kauffman (Editor), Lewis D. Ludwig (Editor)
Hardcover | 29 December 2020 | Edition Number 1
At a Glance
954 Pages
25.4 x 17.8 x 5.6
Hardcover
RRP $462.00
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"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject."
- Ed Witten, Recipient of the Fields Medal
"I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It's a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field."
- Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis
Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers.
Features
- Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers
- Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees
- Edited and contributed by top researchers in the field of knot theory
Industry Reviews
"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject."
- Ed Witten, Recipient of the Fields Medal
"I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It's a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field."
- Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis
"An encyclopedia is expected to be comprehensive, and to include independent expository articles on many topics. The Encyclopedia of Knot Theory is all this. This book will be an excellent introduction to topics in the field of knot theory for advanced undergraduates, graduate students, and researchers interested in knots from many directions."
- MAA Reviews
"Knot theory is an area of mathematics that requires no introduction, and while this massive tome is certainly no introductory text, it does give a panoramic - and, well, encyclopaedic - view of this vast subject.
[. . . ] A book with such an ambitious remit is bound to contain omissions and oddities. [. . .] But this is a small point compared to what has been achieved by this encyclopaedia, which would make a fine addition to any personal or departmental library, or to a departmental coffee table."
- London Mathematical Society
The Encyclopedia of Knot Theory is close to 1000 pages, and every section, article, paragraph, and sentence inspires the reader to want to learn more knot theory. A wonderful attribute of this text is the reference section at the end of each article as opposed to the end of the book. This allows readers to highlight different sources that will allow them to dive deeper into the topic of that section. [. . .] And while it is nearly impossible to include discussions of every branch of the knot theorytree, the editors made a great choice to focus on current topics showing how the area is still a living subject.
[. . .] As a knot theory enthusiast, I truly enjoyed reading about topics I was more familiar with while also exploring topics that were new to me. As an educator, I am excited to share this book with my students and encourage them to read more articles on the topics. Some of the articles in the book include thoughtful open questions for researchers in the field to enjoy, while also providing background for anyone new to knot theory research to use as a foundation. All in all, I loved this text.
- American Mathematical Monthly
I Introduction and History of Knots. 1. Introduction to Knots. II Standard and Nonstandard Representations of Knots. 2. Link Diagrams. 3. Gauss Diagrams. 4. DT Codes. 5. Knot Mosaics. 6. Arc Presentations of Knots and Links. 7. Diagrammatic Representations of Knots and Links as Closed Braids. 8. Knots in Flows. 9. Multi-Crossing Number of Knots and Links. 10. Complementary Regions of Knot and Link Diagrams. 11. Knot Tabulation. III Tangles. 12. What Is a Tangle? 13. Rational and Non-Rational Tangles. 14. Persistent Invariants of Tangles. IV Types of Knots. 15. Torus Knots. 16. Rational Knots and Their Generalizations. 17. Arborescent Knots and Links. 18. Satellite Knots. 19. Hyperbolic Knots and Links. 20. Alternating Knots. 21. Periodic Knots. V Knots and Surfaces. 22. Seifert Surfaces and Genus. 23. Non-Orientable Spanning Surfaces for Knots. 24. State Surfaces of Links. 25. Turaev Surfaces. VI Invariants Defined in Terms of Min and Max. 26. Crossing Numbers. 27. The Bridge Number of a Knot. 28. Alternating Distances of Knots. 29. Superinvariants of Knots and Links. VII Other Knotlike Objects. 30. Virtual Knot Theory. 31. Virtual Knots and Surfaces. 32. Virtual Knots and Parity. 33. Forbidden Moves,Welded Knots and Virtual Unknotting. 34. Virtual Strings and Free Knots. 35. Abstract and Twisted Links. 36. What Is a Knotoid? 37. What Is a Braidoid? 38. What Is a Singular Knot? 39. Pseudoknots and Singular Knots. 40. An Introduction to the World of Legendrian and Transverse Knots 41. Classical Invariants of Legendrian and Transverse Knots. 42. Ruling and Augmentation Invariants of Legendrian Knots. VIII Higher Dimensional Knot Theory. 43. Broken Surface Diagrams and Roseman Moves. 44. Movies and Movie Moves. 45. Surface Braids and Braid Charts. 46. Marked Graph Diagrams and Yoshikawa Moves. 47. Knot Groups. 48. Concordance Groups. IX Spatial Graph Theory. 49. Spatial Graphs. 50. A Brief Survey on Intrinsically Knotted and Linked Graphs. 51. Chirality in Graphs. 52. Symmetries of Graphs Embedded in Sa¶? and Other 3-Manifolds. 53. Invariants of Spatial Graphs. 54. Legendrian Spatial Graphs. 55. Linear Embeddings of Spatial Graphs. 56. Abstractly Planar Spatial Graphs. X Quantum Link Invariants. 57. Quantum Link Invariants. 58. Satellite and Quantum Invariants. 59. Quantum Link Invariants: From QYBE and Braided Tensor Categories. 60. Knot Theory and Statistical Mechanics. XI Polynomial Invariants. 61. What Is the Kauffman Bracket? 62. Span of the Kauffman Bracket and the Tait Conjectures. 63. Skein Modules of 3-Manifold. 64. The Conway Polynomial. 65. Twisted Alexander Polynomials. 66. The HOMFLYPT Polynomial. 67. The Kauffman Polynomials. 68. Kauffman Polynomial on Graphs. 69. Kauffman Bracket Skein Modules of 3-Manifolds. XII Homological Invariants. 70. Khovanov Link Homology. 71. A Short Survey on Knot Floer Homolog. 72. An Introduction to Grid Homology. 73. Categorification. 74. Khovanov Homology and the Jones Polynomial. 75. Virtual Khovanov Homology. XIII Algebraic and Combinatorial Invariants. 76. Knot Colorings. 77. Quandle Cocycle Invariants. 78. Kei and Symmetric Quandles. 79. Racks, Biquandles and Biracks. 80. Quantum Invariants via Hopf Algebras and Solutions to the Yang-Baxter Equation. 81. The Temperley-Lieb Algebra and Planar Algebras. 82. Vassiliev/Finite Type Invariants. 83. Linking Number and Milnor Invariants. XIV Physical Knot Theory. 84. Stick Number for Knots and Links. 85. Random Knots. 86. Open Knots. 87. Random and Polygonal Spatial Graphs. 88. Folded Ribbon Knots in the Plane. XV Knots and Science. 89. DNA Knots and Links. 90. Protein Knots, Links, and Non-Planar Graphs. 91. Synthetic Molecular Knots and Links.
ISBN: 9781138297845
ISBN-10: 1138297844
Published: 29th December 2020
Format: Hardcover
Language: English
Number of Pages: 954
Audience: General Adult
Publisher: Taylor & Francis Ltd
Country of Publication: GB
Edition Number: 1
Dimensions (cm): 25.4 x 17.8 x 5.6
Weight (kg): 2.76
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