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 Webster, Ben (Benjamin Thomas), author.
 Providence, Rhode Island : American Mathematical Society, 2017.
 Description
 Book — 1 online resource (pages cm.)
 Summary

 Chapter 1. Introduction Chapter 2. Categorification of quantum groups Chapter 3. Cyclotomic quotients Chapter 4. The tensor product algebras Chapter 5. Standard modules Chapter 6. Braiding functors Chapter 7. Rigidity structures Chapter 8. Knot invariants Chapter 9. Comparison to category $\mathcal O$ and other knot homologies
 Kamada, Seiichi, 1964 author.
 Singapore : Springer, 2017.
 Description
 Book — 1 online resource ( xi, 212 pages) : illustrations.
 Summary

 1 Surfaceknots. 2 Knots. 3 Motion pictures. 4 Surface diagrams. 5 Handle surgery and ribbon surfaceknots. 6 Spinning construction. 7 Knot concordance. 8 Quandles. 9 Quandle homology groups and invariants. 10 2Dimensional braids. Bibliography. Epilogue. Index.
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(source: Nielsen Book Data)
 Online

 EBSCOhost Access limited to 1 user
 Google Books (Full view)
 Dye, Heather A., author.
 Boca Raton : CRC Press, Taylor & Francis Group, [2016]
 Description
 Book — xxx, 256 pages : illustrations ; 27 cm
 Summary

 Knots and crossings Virtual knots and links CURVES IN THE PLANE VIRTUAL LINKS ORIENTED VIRTUAL LINK DIAGRAMS
 Linking invariants CONDITIONAL STATEMENTS WRITHE AND LINKING NUMBER DIFFERENCE NUMBER CROSSING WEIGHT NUMBERS
 A multiverse of knots FLAT AND FREE LINKS WELDED, SINGULAR, AND PSEUDO KNOTS NEW KNOT THEORIES
 Crossing invariants CROSSING NUMBERS UNKNOTTING NUMBERS UNKNOTTING SEQUENCE NUMBERS
 Constructing knots SYMMETRY TANGLES, MUTATION, AND PERIODIC LINKS PERIODIC LINKS AND SATELLITE KNOTS
 Knot polynomials The bracket polynomial THE NORMALIZED KAUFFMAN BRACKET POLYNOMIAL THE STATE SUM THE IMAGE OF THE FPOLYNOMIAL
 Surfaces SURFACES CONSTRUCTIONS OF VIRTUAL LINKS GENUS OF A VIRTUAL LINK
 Bracket polynomial II STATES AND THE BOUNDARY PROPERTY PROPER STATES DIAGRAMS WITH ONE VIRTUAL CROSSING
 The checkerboard framing CHECKERBOARD FRAMINGS CUT POINTS EXTENDING THE KAUFFMANMURASUGITHISTLETHWAITE THEOREM
 Modifications of the bracket polynomial THE FLAT BRACKET THE ARROW POLYNOMIAL VASSILIEV INVARIANTS
 Algebraic structures Quandles TRICOLORING QUANDLES KNOT QUANDLES
 Knots and quandles A LITTLE LINEAR ALGEBRA AND THE TREFOIL THE DETERMINANT OF A KNOT THE ALEXANDER POLYNOMIAL THE FUNDAMENTAL GROUP
 Biquandles THE BIQUANDLE STRUCTURE THE GENERALIZED ALEXANDER POLYNOMIAL
 Gauss diagrams GAUSS WORDS AND DIAGRAMS PARITY AND PARITY INVARIANTS CROSSING WEIGHT NUMBER
 Applications QUANTUM COMPUTATION TEXTILES
 Appendix A: Tables Appendix B: References by Chapter
 Open problems and projects appear at the end of each chapter.
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(source: Nielsen Book Data)
Science Library (Li and Ma)
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QA612.2 .D94 2016  Unknown 
5. Knots [2014]
 Burde, Gerhard, 1931 author.
 3rd, fully revised and extended edition.  Berlin ; Boston : De Gruyter, [2014].
 Description
 Book — xiii, 417 pages : illustrations ; 25 cm.
 Summary

This 3. edition is an introduction to classical knot theory. It contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups and some basic results of combinatorial group theory are assumed to be known.
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QA612.2 .B87 2014  Unknown 
 Manturov, V. O. (Vasiliĭ Olegovich)
 Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2013.
 Description
 Book — xxv, 521 p. : ill.
 Summary

 Basic Definitions and Notions
 Virtual Knots and ThreeDimensional Topology
 Quandles (Distributive Groupoids) in Virtual Knot Theory
 The Jones Polynomial. Atoms
 Khovanov Homology
 Virtual Braids
 Vassiliev's Invariants
 Parity in Knot Theory. FreeKnots. Cobordisms
 Theory of GraphLinks.
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7. Knot theory & its applications [1996]
 Musubime riron to sono ōyō. English
 Murasugi, Kunio, 1929 author.
 Boston : Birkhäuser, ©2008.
 Description
 Book — 1 online resource (341 pages) : illustrations Digital: text file.PDF.
 Summary

 Introduction. Fundamental Concepts of Knot Theory. Knot Tables. Fundamental Problems of Knot Theory. Classical Knot Invariants. Seifert Matrices. Invariants from the Seifert matrix. Torus Knots. Creating Manifolds from Knots. Tangles and 2Bridge Knots. The Theory of Braids. The Jones Revolution. Knots via Statistical Mechanics. Knot Theory in Molecular Biology. Graph Theory Applied to Chemistry. Vassiliev Invariants. Appendix. Notes. Bibliograph. Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Musubime riron to sono ōyō. English
 Murasugi, Kunio, 1929
 Boston : Birkhäuser, c2008.
 Description
 Book — 341 p. : ill.
 Singapore ; Hackensack, N.J. : World Scientific, c2005.
 Description
 Book — xix, 606 p. : ill.
 Summary

 On the theory of solid knots / Otto Krotenheerdt and Sigrid Veit (translated by Ted Ashton)
 A tutorial on knot energies / E. J. Janse van Rensburg
 Universal energy spectrum of tight knots and links in physics / Roman V. Buniy and Thomas W. Kephart
 Knot dynamics in a driven hanging chain: Experimental results / Andrew Belmonte
 Biarcs, global radius of curvature, and the computation of ideal knot shapes (4 color plates) / M. Carlen, B. Laurie, J. H. Maddocks and J. Smutny
 Knotted umbilical cords (2 color plates) / Alain Goriely
 Modelling DNA as a flexible thick polymer: DNA elasticity and packaging thermodynamics / Cristian Micheletti and Davide Marenduzzo
 MonteCarlo simulations of gelelectrophoresis of DNA knots / C. Weber, M. Fleurant, P. De Los Rios and G. Dietler
 Atomic force microscopy of complex DNA knots / F. Valle, M. Favre, J. Roca and G. Dietler
 Protein folds, knots and tangles / William R. Taylor
 Tying down open knots: A statistical method for identifying open knots with applications to proteins (7 color plates)/ Kenneth C. Millett and Benjamin M. Sheldon
 Scaling of the average crossing number in equilateral random walks, knots and proteins / Akos Dobay, Jacques Dubochet, Andrzej Stasiak and Yuanan Diao
 Folding complexity in a randomwalk copolymer model / Gustavo A. Arteca
 Universal characteristics of polygonal knot probabilities / Kenneth C. Millett and Eric J. Rawdon
 The average crossing number of Gaussian random walks and polygons / Yuanan Diao and Clam Ernst
 Ropelength of tight polygonal knots / Justyna Baransku, Piotr Pieranski and Eric J.Rawdon
 A fast octreebased algorithm for computing ropelength / Ted Ashton and Jason Cantarella
 Topological entropic force between a pair of random knots forming a fixed link / Tetsuo Deguchi
 Underknotted and overknotted polymers: 1. Unrestricted loops / Nathan T. Moore, Rhonald C. Lua and Alexander Yu. Grosberg
 Underknotted and overknotted polymers: 2. Compact selfavoiding loops / Rhonald C. h a , Nathan T. Moore and Alexander Yu. Grosberg
 On the mean gyration radius and the radial distribution function of ring polymers with excluded volume under a topological constraint / Miyuki K. Shimamura and Tetsuo Deguchi
 Thermodynamics and topology of disordered knots. Correlations in trivial lattice knot diagrams / S. K. Nechaev and O. A. Vasilyev
 Generating large random knot projections / Yuanan Diao, Claus Ernst and Uta Ziegler
 Minimal flat knotted ribbons / Louis H. Kauffman
 Quadrisecants of knots with small crossing number / Gyo Taek Jin
 On the writhing number of a nonclosed curve / E. L. Starostin
 On a mathematical model for thick surfaces / Pawet Strzelecki and Heiko von del Mosel
 Some ropelengthcritical clasps / John &I. Sullivan and Nancy C. Wrinkle
 Remarks on Some Hyperbolic Invariants of 2Bridge Knots / Jim Hoste an, d Patrick D. Shanahan
 Conjectures on the enumeration of alternating links / Paul ZinnJustin.
10. Knot theory [2004]
 Manturov, V. O. (Vasiliĭ Olegovich)
 Boca Raton, Fla. : Chapman & Hall/CRC, c2004.
 Description
 Book — 400 p. : ill. ; 25 cm.
 Summary

 I. KNOTS, LINKS, AND INVARIANT POLYNOMIALSINTRODUCTIONBasic DefinitionsREIDEMEISTER MOVES. KNOT ARITHMETICSPolygonal Links and Reidemeister MovesKnot Arithmetics and Seifert SurfacesLINKS IN 2 SURFACES IN R
 3. SIMPLEST LINK INVARIANTSKnots in Surfaces. The Classiffcation of Torus KnotsThe Linking CoefficientThe Arf InvariantThe Colouring InvariantFUNDAMENTAL GROUP. THE KNOT GROUPDigression. Examples of UnknottingFundamental Group. Basic Definitions and ExamplesCalculating Knot GroupsTHE KNOT QUANDLE AND THE CONWAY ALGEBRAIntroductionGeometric and Algebraic Definitions of the QuandleCompleteness of the QuandleSpecial Realisations of the Quandle: Colouring Invariant, Fundamental Group, Alexander PolynomialThe Conway Algebra and Polynomial InvariantsRealisations of the Conway Algebra. The ConwayAlexander, Jones, HOMFLY and Kauffman PolynomialsMore on Alexander's polynomial. Matrix representationKAUFFMAN'S APPROACH TO JONES POLYNOMIALState models in Physics and Kauffman's BracketKauffman's Form of Jones Polynomial and Skein RelationsKauffman's TwoVariable PolynomialPROPERTIES OF JONES POLYNOMIALS. KHOVANOV'S COMPLEXSimplest PropertiesTait's First Conjecture and KauffmanMurasugi's TheoremMenascoThistletwaite Theorem and the Classification of Alternating LinksThe Third Tait ConjectureA Knot TableKhovanov's Categorification of the Jones PolynomialThe Two Phenomenological ConjecturesII. THEORY OF BRAIDSBraids, Links and Representations of Braid GroupsFour Definitions of the Braid GroupLinks as Braid ClosuresBraids and the Jones PolynomialRepresentations of the Braid GroupsThe KrammerBigelow RepresentationBRAIDS AND LINKS. BRAID CONSTRUCTION ALGORITHMSAlexander's TheoremVogel's AlgorithmALGORITHMS OF BRAID RECOGNITIONThe Curve Algorithm for Braid RecognitionLDSystems and the Dehornoy AlgorithmMinimal Word Problem for Br(3)Spherical, Cylindrical, and other BraidsMARKOV'S THEOREM. THE YANGBAXTER EQUATIONMarkov's Theorem after MORTONMakanin's Generalisations. Unary BraidsYangBaxter Equation, Braid Groups and Link InvariantsIII. VASSILIEV'S INVARIANTSDefinition and Basic Notions of Vassiliev Invariant TheorySingular Knots and the Definition of FiniteType InvariantsInvariants of Orders Zero and OneExamples of HigherOrder InvariantsSymbols of Vassiliev's Invariants Coming from the Conway PolynomialOther Polynomials and Vassiliev's InvariantsAn Example of an InfiniteOrder InvariantTHE CHORD DIAGRAM ALGEBRABasic StructuresBialgebra Structure of Algebras A c and A t. Chord Diagrams and Feynman diagramsLie Algebra Representations, Chord Diagrams, and the Four Colour TheoremDimension estimates for Ad. A Table of Known DimensionsTHE KONTSEVICH INTEGRAL AND FORMULAE FOR THE VASSILIEV INVARIANTS209Preliminary Kontsevich IntegralZ(8) and the NormalisationCoproduct for Feynman DiagramsInvariance of the Kontsev.
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(source: Nielsen Book Data)
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QA612.2 .M36 2004  Unknown 
11. Die Entstehung der Knotentheorie : Kontexte und Konstruktionen einer modernen mathematischen Theorie [1999]
 Epple, Moritz.
 Braunschweig/Wiesbaden : Vieweg, c1999.
 Description
 Book — xv, 449 p. : ill. ; 24 cm.
 Online
SAL3 (offcampus storage)
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QA612.2 .E66 1999  Available 
 Lamm, Christoph.
 Bonn : [Mathematisches Institut der Universität Bonn], 1999.
 Description
 Book — vi, 90 p. : ill. ; 21 cm.
 Online
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QA1 .B763 V.321  Available 
13. Ideal knots [electronic resource] [1998]
 Singapore ; River Edge, N.J. : World Scientific Pub. Co., c1998.
 Description
 Book — x, 414 p. : ill.
 Summary

 Ideal knots and their relation to the physics of real knots, A, Stasiak et al
 knots with minimal energies, Y. Diao et al
 the writhe of knots and links, E.J. Janse van Rensburg et al
 entropy of a knot  simple arguments about difficult problems, A. Yu Grosberg
 knots and fluid dynamics, H.K. Moffatt
 mobiusinvariant knot energies, R.B. Kusner and J.M. Sullivan
 fourier knots, L.H. Kauffmann. (Part contents).
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
14. An introduction to knot theory [1997]
 Lickorish, W. B. Raymond.
 New York : Springer, c1997.
 Description
 Book — x, 201 p. : ill. ; 24 cm.
 Summary

 A beginning for Knot Theory. Seifert surfaces and knot factorization. The Jones polynomial. Geometry of alternating links. The Jones polynomial of an alternating link. The Alexander polynomial. Covering spaces. The Conway polynomial, signatures and slice knots. Cylic branched covers and the Goeritz matrix. The Arf invariant and the Jones polynomial. The fundamental group. Obtaining threemanifolds by surgery on S3. Threemanifold invariants from the Jones polynomial. Methods for calculating quantum invariants. Generalizations of the Jones polynomial. Exploring the HOMFLY and Kauffman polynomials.
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Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

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QA612.2 .L53 1997  Unknown 
15. Knot theory and its applications [1996]
 Murasugi, Kunio, 1929
 Boston : Birkhäuser, 1996.
 Description
 Book — 341 p. : ill. ; 24 cm.
 Summary

This text contains most of the fundamental classical facts about knot theory, including: knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces.
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QA612.2 .M8613 1996  Unknown 
 Adams, Colin Conrad.
 New York : W.H. Freeman, c1994.
 Description
 Book — xiii, 306 p. : ill. ; 25 cm.
 Summary

If you are a student of mathematics, a scientist working in fields affected by knot theory research, or a curious amateur who finds mathematics intriguing, The Knot Book is for you. With this engagingly written and illustrated book, you will be working with some of the most advanced ideas in contemporary mathematics.
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 Online
Science Library (Li and Ma)
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QA612.2 .A33 1994  Unknown 
17. Knot theory [1993]
 Livingston, Charles.
 Washington, DC : Mathematical Association of America, c1993.
 Description
 Book — xviii, 240 p. : ill. ; 20 cm.
 Summary

 Acknowledgements
 Preface
 1. A century of knot theory
 2. What is a knot?
 3. Combinatorial techniques
 4. Geometric techniques
 5. Algebraic techniques
 6. Geometry, algebra, and the alexander polynomial
 7. Numerical invariants
 8. Symmetries of knots
 9. Highdimensional knot theory
 10. New combinatorial techniques
 Appendices
 References
 Index.
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(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

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QA612.2 .L585 1993  Unknown 
18. Knot theory [electronic resource] [1993]
 Livingston, Charles.
 Washington, DC : Mathematical Association of America, c1993
 Description
 Book — 1 online resource (xviii, 240 p. : ill).
 Summary

 Preface Chapter 1. A century of knot theory Chapter 2. What is a knot? Chapter 3. Combinatorial techniques Chapter 4. Geometric techniques Chapter 5. Algebraic techniques Chapter 6. Geometry, algebra, and the Alexander polynomial Chapter 7. Numerical invariants Chapter 8. Symmetries of knots Chapter 9. Highdimensional knot theory Chapter 10. New combinatorial techniques Knot table Alexander polynomials References
19. Coloring knots [videorecording] [1992]
 Cappell, Sylvain E.
 Providence, R.I. : American Mathematical Society, c1992.
 Description
 Video — 1 videocassette (ca 60 min.) : sd., col. ; 1/2 in.
 Summary

Describes some of the deep connections between knots and abstract mathematics. Shows how the technique of coloring different segments of knots provides a simple way to bring in some of the main ideas of the subject.
 Online
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ZVC 19558  Unknown 
20. The geometry and physics of knots [1990]
 Atiyah, Michael Francis, 19292019
 Cambridge ; New York : Cambridge University Press, 1990.
 Description
 Book — x, 78 p. ; 23 cm.
 Summary

 Preface
 1. History and background
 2. Topological quantum field theories
 3. Nonabelian moduli spaces
 4. Symplectic quotients
 5. The infinitedimensional case
 6. Projective flatness
 7. The Feynman integral formulation
 8. Final comments
 Bibliography
 Index.
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(source: Nielsen Book Data)
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QA612.2 .A85 1990  Available 
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