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Encyclopedia of Knot Theory

Edited by: Colin Adams , Erica Flapan , Allison Henrich , Louis H. Kauffman , Lewis D. Ludwig , Sam Nelson

Print publication date:  December  2020
Online publication date:  February  2021

Print ISBN: 9781138297845
eBook ISBN: 9781138298217
Adobe ISBN:

 Cite  Marc Record

Book description

"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.


  • 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

Table of contents

Prelims Download PDF
Chapter  1:  Introduction to Knots Download PDF
Chapter  2:  Link Diagrams Download PDF
Chapter  3:  Gauss Diagrams Download PDF
Chapter  4:  DT Codes Download PDF
Chapter  5:  Knot Mosaics Download PDF
Chapter  6:  Arc Presentations of Knots and Links Download PDF
Chapter  7:  Diagrammatic Representations of Knots and Links as Closed Braids Download PDF
Chapter  8:  Knots in Flows Download PDF
Chapter  9:  Multi-Crossing Number of Knots and Links Download PDF
Chapter  10:  Complementary Regions of Knot and Link Diagrams Download PDF
Chapter  11:  Knot Tabulation Download PDF
Chapter  12:  What Is a Tangle? Download PDF
Chapter  13:  Rational and Non-Rational Tangles Download PDF
Chapter  14:  Persistent Invariants of Tangles Download PDF
Chapter  15:  Torus Knots Download PDF
Chapter  16:  Rational Knots and Their Generalizations Download PDF
Chapter  17:  Arborescent Knots and Links Download PDF
Chapter  18:  Satellite Knots Download PDF
Chapter  19:  Hyperbolic Knots and Links Download PDF
Chapter  20:  Alternating Knots Download PDF
Chapter  21:  Periodic Knots Download PDF
Chapter  22:  Seifert Surfaces and Genus Download PDF
Chapter  23:  Non-Orientable Spanning Surfaces for Knots Download PDF
Chapter  24:  State Surfaces of Links Download PDF
Chapter  25:  Turaev Surfaces Download PDF
Chapter  26:  Crossing Numbers Download PDF
Chapter  27:  The Bridge Number of a Knot Download PDF
Chapter  28:  Alternating Distances of Knots Download PDF
Chapter  29:  Superinvariants of Knots and Links Download PDF
Chapter  30:  Virtual Knot Theory Download PDF
Chapter  31:  Virtual Knots and Surfaces Download PDF
Chapter  32:  Virtual Knots and Parity Download PDF
Chapter  33:  Forbidden Moves, Welded Knots and Virtual Unknotting Download PDF
Chapter  34:  Virtual Strings and Free Knots Download PDF
Chapter  35:  Abstract and Twisted Links Download PDF
Chapter  36:  What Is a Knotoid? Download PDF
Chapter  37:  What Is a Braidoid? Download PDF
Chapter  38:  What Is a Singular Knot? Download PDF
Chapter  39:  Pseudoknots and Singular Knots Download PDF
Chapter  40:  An Introduction to the World of Legendrian and Transverse Knots Download PDF
Chapter  41:  Classical Invariants of Legendrian and Transverse Knots Download PDF
Chapter  42:  Ruling and Augmentation Invariants of Legendrian Knots Download PDF
Chapter  43:  Broken Surface Diagrams and Roseman Moves Download PDF
Chapter  44:  Movies and Movie Moves Download PDF
Chapter  45:  Surface Braids and Braid Charts Download PDF
Chapter  46:  Marked Graph Diagrams and Yoshikawa Moves Download PDF
Chapter  47:  Knot Groups Download PDF
Chapter  48:  Concordance Groups Download PDF
Chapter  49:  Spatial Graphs Download PDF
Chapter  50:  A Brief Survey on Intrinsically Knotted and Linked Graphs Download PDF
Chapter  51:  Chirality in Graphs Download PDF
Chapter  52:  Symmetries of Graphs Embedded in S and Other 3-Manifolds Download PDF
Chapter  53:  Invariants of Spatial Graphs Download PDF
Chapter  54:  Legendrian Spatial Graphs Download PDF
Chapter  55:  Linear Embeddings of Spatial Graphs Download PDF
Chapter  56:  Abstractly Planar Spatial Graphs Download PDF
Chapter  57:  Quantum Link Invariants Download PDF
Chapter  58:  Satellite and Quantum Invariants Download PDF
Chapter  59:  Quantum Link Invariants: From QYBE and Braided Tensor Categories Download PDF
Chapter  60:  Knot Theory and Statistical Mechanics Download PDF
Chapter  61:  What Is the Kauffman Bracket? Download PDF
Chapter  62:  Span of the Kauffman Bracket and the Tait Conjectures Download PDF
Chapter  63:  Skein Modules of 3-Manifolds Download PDF
Chapter  64:  The Conway Polynomial Download PDF
Chapter  65:  Twisted Alexander Polynomials Download PDF
Chapter  66:  The HOMFLYPT Polynomial Download PDF
Chapter  67:  The Kauffman Polynomials Download PDF
Chapter  68:  Kauffman Polynomial on Graphs Download PDF
Chapter  69:  Kauffman Bracket Skein Modules of 3-Manifolds Download PDF
Chapter  70:  Khovanov Link Homology Download PDF
Chapter  71:  A Short Survey on Knot Floer Homology Download PDF
Chapter  72:  An Introduction to Grid Homology Download PDF
Chapter  73:  Categorification Download PDF
Chapter  74:  Khovanov Homology and the Jones Polynomial Download PDF
Chapter  75:  Virtual Khovanov Homology Download PDF
Chapter  76:  Knot Colorings Download PDF
Chapter  77:  Quandle Cocycle Invariants Download PDF
Chapter  78:  Kei and Symmetric Quandles Download PDF
Chapter  79:  Racks, Biquandles and Biracks Download PDF
Chapter  80:  Quantum Invariants via Hopf Algebras and Solutions to the Yang-Baxter Equation Download PDF
Chapter  81:  The Temperley-Lieb Algebra and Planar Algebras Download PDF
Chapter  82:  Vassiliev/Finite-Type Invariants Download PDF
Chapter  83:  Linking Number and Milnor Invariants Download PDF
Chapter  84:  Stick Number for Knots and Links Download PDF
Chapter  85:  Random Knots Download PDF
Chapter  86:  Open Knots Download PDF
Chapter  87:  Random and Polygonal Spatial Graphs Download PDF
Chapter  88:  Folded Ribbon Knots in the Plane Download PDF
Chapter  89:  DNA Knots and Links Download PDF
Chapter  90:  Protein Knots, Links and Non-Planar Graphs Download PDF
Chapter  91:  Synthetic Molecular Knots and Links Download PDF
Index Download PDF
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