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adams colin (curatore); flapan erica (curatore); henrich allison (curatore); kauffman louis h. (curatore); ludwig lewis d. (curatore); nelson sam (curatore) - encyclopedia of knot theory

Encyclopedia of Knot Theory

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Lingua: Inglese
Pubblicazione: 12/2020
Edizione: 1° edizione

Note Editore

"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


I Introduction and History of Knots Chapter 1. Introduction to Knots Lewis D. Ludwig II Standard and Nonstandard Representations of Knots Chapter 2. Link Diagrams Jim Hoste Chapter 3. Gauss Diagrams Inga Johnson Chapter 4. DT Codes Heather M. Russell Chapter 5. Knot Mosaics Lewis D. Ludwig Chapter 6. Arc Presentations of Knots and Links Hwa Jeong Lee Chapter 7. Diagrammatic Representations of Knots and Links as Closed Braids Sofia Lambropoulou Chapter 8. Knots in Flows Michael C. Sullivan Chapter 9. Multi-Crossing Number of Knots and Links Colin Adams Chapter 10. Complementary Regions of Knot and Link Diagrams Colin Adams Chapter 11. Knot Tabulation Jim Hoste III Tangles Chapter 12. What Is a Tangle? Emille Davie Lawrence Chapter 13. Rational and Non-Rational Tangles Emille Davie Lawrence Chapter 14. Persistent Invariants of Tangles Daniel S. Silver and Susan G. Williams IV Types of Knots Chapter 15. Torus Knots Jason Callahan Chapter 16. Rational Knots and Their Generalizations Robin T. Wilson Chapter 17. Arborescent Knots and Links Francis Bonahon Chapter 18. Satellite Knots Jennifer Schultens Chapter 19. Hyperbolic Knots and Links Colin Adams Chapter 20. Alternating Knots William W. Menasco Chapter 21. Periodic Knots Swatee Naik V Knots and Surfaces Chapter 22. Seifert Surfaces and Genus Mark Brittenham Chapter 23. Non-Orientable Spanning Surfaces for Knots Thomas Kindred Chapter 24. State Surfaces of LinksEfstratia Kalfagianni Chapter 25. Turaev Surfaces Seungwon Kim and Ilya Kofman VI Invariants Defined in Terms of Min and Max Chapter 26. Crossing Numbers Alexander Zupan Chapter 27. The Bridge Number of a Knot Jennifer Schultens Chapter 28. Alternating Distances of Knots Adam Lowrance Chapter 29. Superinvariants of Knots and Links Colin Adams VII Other Knotlike Objects Chapter 30. Virtual Knot Theory Louis H. Kauffman Chapter 31. Virtual Knots and Surfaces Micah Chrisman Chapter 32. Virtual Knots and Parity Heather A. Dye and Aaron Kaestner Chapter 33. Forbidden Moves, Welded Knots and Virtual Unknotting Sam Nelson Chapter 34. Virtual Strings and Free Knots Nicolas Petit Chapter 35. Abstract and Twisted Links Naoko Kamada Chapter 36. What Is a Knotoid? Harrison Chapman Chapter 37. What Is a Braidoid? Neslihan Gugumcu Chapter 38. What Is a Singular Knot? Zsuzsanna Dancso Chapter 39. Pseudoknots and Singular Knots Inga Johnson Chapter 40. An Introduction to the World of Legendrian and Transverse Knots Lisa Traynor Chapter 41. Classical Invariants of Legendrian and Transverse Knots Patricia Cahn Chapter 42. Ruling and Augmentation Invariants of Legendrian Knots Joshua M. Sabloff VIII Higher Dimensional Knot Theory Chapter 43. Broken Surface Diagrams and Roseman Moves J. Scott Carter and Masahico Saito Chapter 44. Movies and Movie Moves J. Scott Carter and Masahico Saito Chapter 45. Surface Braids and Braid Charts Seiichi Kamada Chapter 46. Marked Graph Diagrams and Yoshikawa Moves Sang Youl Lee Chapter 47. Knot Groups Alexander Zupan Chapter 48. Concordance Groups Kate Kearney IX Spatial Graph Theory Chapter 49. Spatial Graphs Stefan Friedl and Gerrit Herrmann Chapter 50. A Brief Survey on Intrinsically Knotted and Linked Graphs Ramin Naimi Chapter 51. Chirality in Graphs Hugh Howards Chapter 52. Symmetries of Graphs Embedded in S? and Other 3-Manifolds Erica Flapan Chapter 53. Invariants of Spatial Graphs Blake Mellor Chapter 54. Legendrian Spatial Graphs Danielle O’Donnol Chapter 55. Linear Embeddings of Spatial Graphs Elena Pavelescu Chapter 56. Abstractly Planar Spatial Graphs Scott A. Taylor X Quantum Link Invariants Chapter 57. Quantum Link InvariantsD. N. Yetter Chapter 58. Satellite and Quantum Invariants H. R. Morton Chapter 59. Quantum Link Invariants: From QYBE and Braided Tensor Categories Ruth Lawrence Chapter 60. Knot Theory and Statistical Mechanics Louis H. Kauffman XI Polynomial Invariants Chapter 61. What Is the Kauffman Bracket? Charles Frohman Chapter 62. Span of the Kauffman Bracket and the Tait Conjectures Neal Stoltzfus Chapter 63. Skein Modules of 3-Manifold Rhea Palak Bakshi, Jozef H. Przytycki and Helen Wong Chapter 64. The Conway Polynomial Sergei Chmutov Chapter 65. Twisted Alexander Polynomials Stefano Vidussi Chapter 66. The HOMFLYPT Polynomial Jim Hoste Chapter 67. The Kauffman Polynomials Jianyuan K. Zhong Chapter 68. Kauffman Polynomial on Graphs Carmen Caprau Chapter 69. Kauffman Bracket Skein Modules of 3-Manifolds Rhea Palak Bakshi, Jozef Przytycki and Helen Wong XII Homological Invariants Chapter 70. Khovanov Link Homology Radmila Sazdanovic Chapter 71. A Short Survey on Knot Floer Homology Andras I. Stipsicz Chapter 72. An Introduction to Grid Homology Andras I. Stipsicz Chapter 73. Categorification Volodymyr MazorchukChapter 74. Khovanov Homology and the Jones Polynomial Alexander N. Shumakovitch Chapter 75. Virtual Khovanov Homology William Rushworth XIII Algebraic and Combinatorial Invariants Chapter 76. Knot Colorings Pedro Lopes Chapter 77. Quandle Cocycle Invariants J. Scott Carter Chapter 78. Kei and Symmetric Quandles Kanako Oshiro Chapter 79. Racks, Biquandles and Biracks Sam Nelson Chapter 80. Quantum Invariants via Hopf Algebras and Solutions to the Yang-Baxter Equation Leandro Vendramin Chapter 81. The Temperley-Lieb Algebra and Planar Algebras Stephen Bigelow Chapter 82. Vassiliev/Finite Type Invariants Sergei Chmutov and Alexander Stoimenow Chapter 83. Linking Number and Milnor Invariants Jean-Baptiste Meilhan XIV Physical Knot Theory Chapter 84. Stick Number for Knots and Links Colin Adams Chapter 85. Random Knots Kenneth Millett Chapter 86. Open KnotsJulien Dorier, Dimos Goundaroulis, Eric J. Rawdon, and Andrzej Stasiak Chapter 87. Random and Polygonal Spatial GraphsKenji Kozai Chapter 88. Folded Ribbon Knots in the Plane Elizabeth Denne XV Knots and Science Chapter 89. DNA Knots and Links Isabel K. Darcy Chapter 90. Protein Knots, Links, and Non-Planar Graphs Helen Wong Chapter 91. Synthetic Molecular Knots and Links Erica Flapan


Colin Adams is the Thomas T. Read Professor of Mathematics at Williams College, having received his Ph.D. from the University of Wisconsin-Madison in 1983 and his Bachelor of Science from MIT in 1978. He is the author or co-author of numerous research papers in knot theory and low-dimensional topology and nine books, including the text The Knot Book", the comic book Why Knot? and the text Introduction to Topology: Pure and Applied. He is a managing editor for the Journal of Knot Theory and its Ramifications and an editor for the recently publishedcKnots, Low Dimensional Topology and Applications, Springer, 2019. A recipient of the Haimo National Distinguished Teaching Award, he has also been an MAA Polya Lecturer, a Sigma Xi Distinguished Lecturer, and a recipient of the Robert Foster Cherry Teaching Award. He has worked with over 130 undergraduates on original research in knot theory and low-dimensional topology. He is also the humor columnist for the expository math magazine, the Mathematical Intelligencer. Erica Flapan was a professor at Pomona College from 1986 to 2018. From 2000 until 2014, Flapan taught at the Summer Mathematics Program for freshmen and sophomore women at Carleton College, and mentored many of those women as they got their PhD’s in mathematics. In 2011, Flapan won the Mathematical Association of America’s Haimo award for distinguished college or university teaching of mathematics. Then in 2012, she was selected as an inaugural fellow of the American Mathematical Society. From 2015-2017, she was a Polya Lecturer for the MAA. Since 2019, she has been the Editor-in-Chief of the Notices of the American Mathematical Society. Erica Flapan has published extensively in topology and its applications to chemistry and molecular biology. In addition to her many research papers, she has published an article in the College Mathematics Journal entitled "How to be a good teacher is an undecidable problem," as well as four books. Her first book, entitled When Topology Meets Chemistry was published jointly by the Mathematical Association of America and Cambridge University Press. Her second book entitled Applications of Knot Theory, is a collection of articles that Flapan co-edited with Professor Dorothy Buck of Imperial College London. Flapan also co-authored a textbook entitled Number Theory: A Lively Introduction with Proofs, Applications, and Stories with James Pommersheim and Tim Marks, published by John Wiley and sons. Finally, in 2016, the AMS published her book entitled Knots, Molecules, and the Universe: An Introduction to Topology, which is aimed at first and second year college students. Allison Henrich is a Professor of Mathematics at Seattle University. She earned her PhD in Mathematics from Dartmouth College in 2008 and her undergraduate degrees in Mathematics and Philosophy from the University of Washington in 2003. Allison has been dedicated to providing undergraduates with high-quality research experiences since she mentored her first group of students in the SMALL REU at Williams College in 2009, under the mentorship of Colin Adams. Since then, she has mentored 35 beginning researchers, both undergraduates and high school students. She has directed and mentored students in the SUMmER REU at Seattle University and has served as a councilor on the Council on Undergraduate Research. In addition, Allison co-authored An Interactive Introduction to Knot Theory for undergraduates interested in exploring knots with a researcher’s mindset, and she co-authored A Mathematician’s Practical Guide to Mentoring Undergraduate Research, a resource for math faculty. Allison is excited about the publication of the Concise Encyclopedia of Knot Theory, as it will be an essential resource for beginning knot theory researchers! Louis H. Kauffman was born in Potsdam, New York on Feb. 3, 1945. As a teenager he developed interests in Boolean algebra, circuits, diagrammatic logic and experiments related to non-linear pendulum oscillations. He received the degree of B.S. in Mathematics from MIT in 1966 and went to Princeton University for graduate school where he was awarded PhD in 1972. At Princeton he studied with William Browder and began working with knots and with singularities of complex hypersurfaces through conversations with the knot theorist Ralph Fox and the lectures of F. Hirzebruch and J. Milnor. From January 1971 to May 2017, he taught at the University of Illinois at Chicago where he is now Emeritus Professor of Mathematics. Kauffman's research is in algebraic topology and particularly in low dimensional topology (knot theory) and its relationships with algebra, logic, combinatorics, mathematical physics and natural science. He is particularly interested in the structure of formal diagrammatic systems such as the system of knot diagrams that is one of the foundational approaches to knot theory. Kauffman’s research in Virtual Knot Theory has opened a new field of knot theory and has resulted in th

Altre Informazioni



Condizione: Nuovo
Dimensioni: 10 x 7 in Ø 5.18 lb
Formato: Copertina rigida
Illustration Notes:485 b/w images, 80 color images and 4 tables
Pagine Arabe: 954

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