内容

目次

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 Links Efstratia 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 3 and Other 3-Manifolds Erica Flapan Chapter 53. Invariants of Spatial Graphs Blake Mellor Chapter 54. 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 Invariants D. 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 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 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 Mazorchuk XIII Algebraic and Combinatorial Invariants Chapter 74. Knot Colorings Pedro Lopes Chapter 75. Quandle Cocycle Invariants J. Scott Carter Chapter 76. Kei and Symmetric Quandles Kanako Oshiro Chapter 77. Racks, Biquandles and Biracks Sam Nelson Chapter 78. Quantum Invariants via Hopf Algebras and Solutions to the Yang-Baxter Equation Leandro Vendramin Chapter 79. The Temperley-Lieb Algebra and Planar Algebras Stephen Bigelow Chapter 80. Vassiliev/Finite Type Invariants Sergei Chmutov and Alexander Stoimenow Chapter 81. Linking Number and Milnor Invariants Jean-Baptiste Meilhan XIV Physical Knot Theory Chapter 82. Stick Number for Knots and Links Colin Adams Chapter 83. Random Knots Kenneth Millett Chapter 84. Open Knots Julien Dorier, Dimos Goundaroulis, Eric J. Rawdon, and Andrzej Stasiak Chapter 85. Random and Polygonal Spatial Graphs Kenji Kozai Chapter 86. Folded Ribbon Knots in the Plane Elizabeth Denne XV Knots and Science Chapter 87. DNA Knots and Links Isabel K. Darcy Chapter 88. Protein Knots, Links, and Non-Planar Graphs Helen Wong Chapter 89. Synthetic Molecular Knots and Links Erica Flapan