81. A Brief History Of Knot Theory: knot theory and DNA. A Brief History of knot theory People have beenstudying, classifying and tying knots for thousands of years. http://www.kpbsd.k12.ak.us/kchs/JimDavis/CalculusWeb/math web page.htm

Knot Theory and DNA A Brief History of Knot Theory: People have been studying, classifying and tying knots for thousands of years. It hasn’t been until the last couple hundred that people have tried to apply this genre of mathematics to science. In the 1800’s, people used Knot Theory to try and explain the elements and how they knot with each other, forming certain patterns. What does DNA have to do with knots? In the 1950’s, Watson and Crick discovered the shape of the DNA molecule was a double helix. It wasn’t until the 1980’s, however, that biologists and chemists found out that DNA can become tangled (or knotted) at times. This led to a rise in Knot Theory and topology (the study of the properties of three-dimensional figures and solids). How does DNA become tangled? Under certain circumstances, DNA loses its helical shape. This can happen when enzymes act upon it. By mutilating the shape of the molecule, enzymes can inhibit the basic functions of DNA that are ultimately necessary for life and include replication to make new cells, coding for proteins that make up our bodies, and recombination in meiosis to create offspring. How complicated do these knots get?

82. KLUWER Academic Publishers | Topics In Knot Theory Books » Topics in knot theory. Topics in knot theory. For mathematicians, graduatestudents and scientists interested in knot theory. Contents and Contributors. http://www.wkap.nl/prod/b/0-7923-2285-1

Title Authors Affiliation ISBN ISSN advanced search search tips Books Topics in Knot Theory Topics in Knot Theory Kluwer Academic Publishers is pleased to make this title available as a special Printing on Demand (PoD) edition. PoD books will be sent to you within 6-9 weeks of receipt of your order. Firm orders only!: returns cannot be accepted as PoD books are only printed on request. Add to cart Proceedings of the NATO Advanced Study Institute, Erzurum, Turkey, September 1-12, 1992 edited by Book Series: NATO SCIENCE SERIES: C: Mathematical and Physical Sciences (continued within NATO SCIENCE SERIES II: Mathematics, Physics and Chemistry Volume 399 Topics in Knot Theory is a state of the art volume which presents surveys of the field by the most famous knot theorists in the world. It also includes the most recent research work by graduate and postgraduate students. The new ideas presented cover racks, imitations, welded braids, wild braids, surgery, computer calculations and plottings, presentations of knot groups and representations of knot and link groups in permutation groups, the complex plane and/or groups of motions. For mathematicians, graduate students and scientists interested in knot theory.

83. Knot Theory - Cambridge University Press Home Catalogue knot theory. Related Areas knot theory. Charles Livingston. £25.00.September 1996 Hardback 258 pages 221 line diagrams ISBN 0883850273. http://books.cambridge.org/0883850273.htm

Home Catalogue Related Areas: Pure Mathematics Carus Mathematical Monographs New titles Email For updates on new titles in: Pure Mathematics Knot Theory Charles Livingston In stock Only for sale in Australia, United Kingdom, Ireland, New Zealand, South Africa, United States of America Knot Theory, a lively exposition of the mathematics of knotting, will appeal to a diverse audience from the undergraduate seeking experience outside the traditional range of studies to mathematicians wanting a leisurely introduction to the subject. Graduate students beginning a program of advanced study will find a worthwhile overview, and the reader will need no training beyond linear algebra to understand the mathematics presented. The interplay between topology and algebra, known as algebraic topology, arises early in the book, when tools from linear algebra and from basic group theory are introduced to study the properties of knots, including one of mathematics’ most beautiful topics, symmetry. The book closes with a discussion of high-dimensional knot theory and a presentation of some of the recent advances in the subject - the Conway, Jones and Kauffman polynomials. A supplementary section presents the fundamental group, which is a centerpiece of algebraic topology. Reviews ‘The author’s book would be a good text for an undergraduate course in knot theory The topics in the book are nicely tied together The topics and the exercises together can provide an opportunity for many undergraduates to get a real taste of what present day mathematics is like.’Mathematical Reviews

84. IIId OPORTO MEETING ON KNOT THEORY AND PHYSICS on. knot theory AND PHYSICS. June 6th8th, 1994. MAIN SPEAKERS and PLANNEDCOURSES. José Sousa RAMOS, (IST, Lisbon) knot theory and dynamical systems. http://www.math.ist.utl.pt/~jmourao/om/om94b.html

IIId OPORTO MEETING on KNOT THEORY AND PHYSICS June 6th-8th, 1994 MAIN SPEAKERS and PLANNED COURSES Jeannette NELSON (INFN Torino, Italy): Knots and the braid group in 2+1 gravity (IST, Lisbon): Knot theory and dynamical systems (FCUP, Oporto): Combinatorial invariants for 3-manifolds (FCUP, Oporto): Topics in topological quantum field theories LIST of SEMINARS Paulo ALMEIDA (IST, Lisbon): Non-commutative geometry via examples Entropy-like invariants and their relationships Alcides CAETANO (FCUL, Lisbon): On the kernel of holonomy Raul CORDOVIL (IST, Lisbon): Braid monodromy groups of wiring diagrams Nenad MANOJLOVIC (Univ. Algarve): Riemann-Hilbert problem and the chiral equations in two dimensions Integration on the space of connections modulo gauge transformations Shingo OKAMOTO (IST, Lisbon): Knot theory and operator algebras Roger PICKEN (IST, Lisbon): Kontsevich integrals and related topics Thomas THIEMANN (Penn State Univ.): Introduction to constructive quantum field theory Robin TUCKER (Lancaster Univ., UK):

85. Ist OPORTO MEETING ON KNOT THEORY AND PHYSICS Translate this page Ist OPORTO MEETING on. knot theory AND PHYSICS. February 24th-27th, 1992. RogerPICKEN, (IST, Lisbon) knot theory and Topological Quantum Field Theories. http://www.math.ist.utl.pt/~jmourao/om/om92b.html

Ist OPORTO MEETING on KNOT THEORY AND PHYSICS February 24th-27th, 1992 MAIN SPEAKERS and PLANNED COURSES Roger PICKEN (IST, Lisbon): Knot Theory and Topological Quantum Field Theories (FCUP, Porto): An Introduction to Knot Theory (FCUP, Porto): Ashtekar Variables in Canonical Gravity ORGANIZING COMMITTEE jmourao@ualg.pt Roger Picken (Lisbon, IST): picken@math.ist.utl.pt jntavar@fc.up.pt jntavar@fc.up.pt Home page address: http://www.fisica.ist.utl.pt/~jmourao/om/om92b.html FINANCIAL SUPPORT Projecto "AGCQ" PBIC/C/MAT/2150/95

86. Classical Knot Theory Classical knot theory. This is one of the sites in Masahico Saito's Home Page. Actuallythere are many more web sites on knot theory with amazing graphics. http://www.math.usf.edu/~saito/classical.html

Classical Knot Theory This is one of the sites in Masahico Saito's Home Page. In the future I like to write about my research on this topic, but until then try the following links. The KnotPlot Site by Robert Scharein Lou Kauffman's home page Mowen Thistlesweit's home page Actually there are many more web sites on knot theory with amazing graphics. After listing the above three, I realized that it's just impossible to list all I want, so I have to stop here for now. Go to the above sites and start surfing.

87. Knot Theory knot theory. Fred Curtis Mar 2001. This What is knot theory? Knottheory is a branch of mathematics dealing with tangled loops. When http://f2.org/maths/kt/

Up to Home Maths Site Map Text version Knot Theory Fred Curtis - Mar 2001] This page is a tiny introduction to Knot Theory. It describes some basic concepts and provides links to my work and other Knot Theory resources. What is Knot Theory? My Interests Old papers I'm typing up References What is Knot Theory? Knot theory is a branch of mathematics dealing with tangled loops. When there's just one loop, it's called a knot . When there's more than one loop, it's called a link and the individual loops are called components of the link. A picture of a knot is called a knot diagram or knot projection . A place where parts of the loop cross over is called a crossing . The simplest knot is the unknot or trivial knot , which can be represented by a loop with no crossings. The big problem in knot theory is finding out whether two knots are the same or different. Two knots are regarded as being the same if they can be moved about in space, without cutting, to look exactly like each other. Such a movement is called an ambient isotopy - the ambient refers to moving the knot through 3-dimensional space, and

88. Knot Theory And Functional Integration Calendar. knot theory and functional integration. Louis H. Kauffman (MSRIEvansTalk) (Scheduled Workshop Talk). Monday, Dec 9, 2002 410 pm to 510 pm http://www.msri.org/calendar/talks/TalkInfo/1508/show_talk

Calendar Knot theory and functional integration Louis H. Kauffman (MSRI-Evans Talk) (Scheduled Workshop Talk) Monday, Dec 9, 2002 4:10 pm to 5:10 pm at Evans Hall, UC Berkeley LOCATION: UC Berkeley Department of Mathematics, Evans Hall Room 60 Parent Workshop: The Feynman Integral Along with Related Topics and Applications MSRI Home Page Search the MSRI Website Subject and Title Index ... webmaster@msri.org

89. Knot Theory Seminar Emeritus knot theory, Spring 2000. Here is a 52 knot. (it was theicon in front of my name in the faculty list.) It is built as http://www.aquinas.edu/homepages/mcdanmic/preview.htm

Emeritus Knot Theory, Spring 2000 Here is a 5-2 knot. (it was the icon in front of my name in the faculty list.) It is built as if it were in a rectangular box. It has more than 5 crossings, but some of the crossings are trivial. Click here for a page on calculating the Jones polynomial Check out this knot-related site: The Knots in Mathematics Exhibit And this one: Scharein's KnotPlot Finding the graphs associated with a knot. This display of Seifert surfaces contained eight models, the work of ten students. The showcase was next to the bookstore Spring `99. (photo: Cathy Lynch.) Five of the surfaces now can be seen in the department offices.

90. Paul Pearson, Northwestern Department Of Mathematics knot theory While at St. Olaf I took a knot theory course for fun. Istudied the properties of torus knots, knots that can be wrapped http://www.math.northwestern.edu/~pearsonp/knottheory.html

Scholarship: C.V. Publications Research Teaching Interests: Algebra Geometry Knot Theory Topology ... Wavelets Knot Theory While at St. Olaf I took a knot theory course for fun. I studied the properties of torus knots, knots that can be wrapped around the surface of a torus without intersections, in a small group. We proved that the (3,5) torus knot (the one in the upper left-hand corner of this page) is the 10 knot and we also determined the determinant of any (p,q) torus knot. Knot theory is a great topic for those with recreational interest (such as my friend who took the course even though she is a piano performance major at St. Olaf) or those with more serious interest (like me). Please e-mail me at p-pearson@northwestern.edu if you are interested in what I am doing or if you have something interesting to share with me. Links Knot Plot Journal of Knot Theory Knot Theory at the Geometry Junkyard math.northwestern.edu/~pearsonp ... p-pearson@northwestern.edu

91. Re: Is "knot Theory" Related To String & M-theory? Re Is knot theory related to string Mtheory? There are indeedinteresting relations between string theory and knot theory. http://www.lns.cornell.edu/spr/1998-12/msg0013810.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index Re: Is "knot theory" related to string & M-theory? Subject : Re: Is "knot theory" related to string & M-theory? From : baez@galaxy.ucr.edu (john baez) Date : 12 Dec 1998 00:00:00 GMT Approved : mmcirvin@world.std.com (sci.physics.research) Newsgroups : sci.physics.research Organization : University of California, Riverside References 36707c49.0@pink.one.net.au Sender : mmcirvin@world.std.com (Matthew J McIrvin) 36707c49.0@pink.one.net.au References Is "knot theory" related to string & M-theory? Or do I have to undergo cold-turkey! :-) From: Prev by Date: Re: This Week's Finds in Mathematical Physics (Week 127) Next by Date: Re: Quantum measurement problem Prev by thread: Is "knot theory" related to string & M-theory? Or do I have to undergo cold-turkey! :-) Next by thread: corona Index(es): Date Thread

92. Is "knot Theory" Related To String & M-theory? Or Do I Have To Undergo C Is knot theory related to string Mtheory? Or do I have to undergo cold-turkey!-). Subject Is knot theory related to string M-theory? http://www.lns.cornell.edu/spr/1998-12/msg0013774.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index Is "knot theory" related to string & M-theory? Or do I have to undergo cold-turkey! :-) Subject : Is "knot theory" related to string & M-theory? Or do I have to undergo cold-turkey! :-) From Date : 11 Dec 1998 00:00:00 GMT Approved : baez@math.ucr.edu Newsgroups : sci.physics.research Organization Follow-Ups Re: Is "knot theory" related to string & M-theory? From: baez@galaxy.ucr.edu (john baez) Prev by Date: Re: vector potential Next by Date: Re: Ether-wind detected! Prev by thread: Re: Where is this cartoon from? Next by thread: Re: Is "knot theory" related to string & M-theory? Index(es): Date Thread

93. Knot Theory knot theory. WT topology FT theorie des noeuds RT combinatorialtopology Previous Item Next Item Search Help. http://www.nrc.ca/irc/thesaurus/knot_theory.html

knot theory WT topology FT theorie des noeuds RT combinatorial topology [Previous Item] [Next Item] [Search] ... [Help]

94. Von Neumann Algebras, Knot Theory, And Quantum Field Theory von Neumann algebras, knot theory, and quantum field theory. Audience Knottheory and the Jonespolynomial. Algebraic quantum field theory. http://remote.science.uva.nl/~npl/vna.html

von Neumann algebras, knot theory, and quantum field theory Audience: 4th year mathematics students, theoretical physics students interested in mathematical physics, PhD students in analysis, mathematical physics, or quantum field theory, staff Prerequisites: Real analysis (Elementary functional analysis and Hilbert space theory, Integration theory). Dates: Tuesdays and Thursdays, 3d trimester (1999); April 6,8,13,20,22,27, May 18,20,25,27, June 1,3,8,10,15,17,22,24 (18 lectures) Place and time: Tuesdays: 11:15-13:00, TF.248 (seminar room of the Institute for Theoretical Physics, 2nd floor), Valckenierstraat 65, 1018 XE AMSTERDAM. Thursdays: 11:15-13:00, WZL.286 (seminar room of the van der Waals-Zeeman lab, , 2nd floor), Valckenierstraat 65, 1018 XE AMSTERDAM. Contents: Algebras of operator algebras on a Hilbert space, C*-algebras and von Neumann algebras. Classification of factors. Subfactors, Jones index. Knot theory and the Jones-polynomial. Algebraic quantum field theory. Superselection rules and subfactors. Literature: V.S. Sunder, An Invitation to von Neumann Algebras (Springer, 1987)

95. Atlas: KNOTS In WASHINGTON XII Conference On Knot Theory And Its Ramifications - KNOTS in WASHINGTON XII Conference on knot theory and its RamificationsMay 1012, 2001 George Washington University Washington DC, USA. http://atlas-conferences.com/c/a/h/j/01.htm

Atlas home Conferences Abstracts Travel ... about Atlas KNOTS in WASHINGTON XII Conference on Knot Theory and its Ramifications May 10-12, 2001 George Washington University Washington DC, USA Conference Organizers Dubravko Ivansic, Ilya Kofman, Jozef H.Przytycki, Yongwu Rong and Akira Yasuhara Conference Homepage View Abstracts This is an archive of abstracts accepted to this conference. For more listing and sorting options, see the dynamic list. Lowell Abrams Frobenius algebras, 2-dimensional surfaces... and knots? Jan Dymara Survey of Tits buildings Kasia Dymara Legendrian knots in overtwisted contact structures Sara Faridi Rees Algebras Bill Goldman The Lie algebra of curves on surfaces Makiko Ishiwata A surgery description of an integral homology three-sphere respecting the Casson invariant Samuel J. Lomonaco, Jr. Invariants of Quantum Entanglement Uwe Kaiser Skein modules, quantum deformations and string topology Louis H Kauffman Infinite number of nontrivial links with trivial Jones polynomial Thomas Kerler Skein theory for the Alexander Polynomial of 3-Manifolds via Hopf algebras Thomas Mattman Seifert surgeries and the (-3, 3, 5) pretzel knot.

96. Atlas: KNOTS In WASHINGTON XIII; Conference On Knot Theory And Its Ramifications Atlas KNOTS in WASHINGTON XIII; Conference on knot theory and its RamificationsDecember 16, 2001 GWU Washington, DC, USA. Conference http://atlas-conferences.com/c/a/i/p/01.htm

Atlas home Conferences Abstracts Travel ... about Atlas KNOTS in WASHINGTON XIII; Conference on Knot Theory and its Ramifications December 16, 2001 GWU Washington, DC, USA Conference Organizers Jozef H. Przytycki (GWU) and Dubravko Ivansic (GWU) View Abstracts This is an archive of abstracts accepted to this conference. For more listing and sorting options, see the dynamic list. Marta Asaeda TQFT arising from subfactor Dubravko Ivansic Interesting Kirby diagrams of the 4-sphere? Samuel J. Lomonaco, Jr. Quantum Computing and Knot Theory Louis H. Kauffman Knots, Vassiliev Invariants and Functional Integration without Integration Thomas Kerler Identifications of Braid Group Representations Jozef H. Przytycki Rotors and the homology of branched double covers of links and tangles Daniel S. Silver 3-Manifolds, Tangles and Persistent Invariant Susan G. Williams Torsion Numbers of Augmented Groups Atlas Conferences Inc.

97. Fantastic Sea Creatures Derived From Knot Theory Fantastic Sea Creatures Derived from knot theory. KnotPlot, RG Scharein. http://www.nsf.gov/od/lpa/forum/colwell/rc2000mitre/tsld010.htm

Fantastic Sea Creatures Derived from Knot Theory KnotPlot, R. G. Scharein Previous slide Next slide Back to first slide View graphic version

98. Felix.unife.it/Root/d-Mathematics/d-Geometry/b-Knot-theory Yale UP 1989 ?. R. Crowell/R. Fox Introduction to knot theory. Ginn 1963. RalphFox Recent developments of knot theory of Princeton. Proc. Int. http://felix.unife.it/Root/d-Mathematics/d-Geometry/b-Knot-theory

Colin Adams: The knot book. An elementary introduction to the mathematical theory of knots. Freeman 1994, 310p. 0-7167-2393-X. $24. [= Das Knotenbuch. Spektrum 1995, 300p. DM 78.] 6940 Colin Adams: Tilings of space by knotted tiles. Math. Intell. 17/2 (1995), 41-51. 7379 Martin Aigner/J. Seidel: Knoten, Spinmodelle und Graphen. Jber. DMV 97 (1995), 75-96. J. Alexander: A lemma on a system of knotted curves. Proc. Nat. Ac. Sci. USA 9 (1923), 93-95. 5884 Emil Artin: Theorie der Zoepfe. Hamb. Abh. 4 (1925), 47-72. [5883 Artin, 416-441] 5885 Emil Artin: Theory of braids. Annals of Math. 48 (1947), 127-136. [5883 Artin, 446-471] 5886 Emil Artin: Braids and permutations. Annals of Math. 48 (1947), 643-649. [5883 Artin, 472-478] 5887 Emil Artin: The theory of braids. American Scientist 38 (1950), 112-119. [5883 Artin, 491-498] 2524 Clifford Ashley: Il grande libro dei nodi. Rizzoli 1989. 890 Michael Atiyah: The frontier between geometry and physics. Jber. DMV 91 (1989), 149-158. R. Baxter: Exactly solved models in statistical mechanics. Academic Press 1982. 2539 Joan Birman: Braids, links and mapping class groups. Princeton UP 1974. 2227 Joan Birman: Recent developments in braid and link theory. Math. Intell. 13/1 (1991), 52-60. 2236 J. Birman/H. Wenzl: Braids, link polynomials and a new algebra. Trans. AMS 313 (1989), 249-273. [3291] 5880 Gerhard Burde/Heiner Zieschang: Knots. De Gruyter 1985, 400p. 3-11-008675-1. DM 140. L. Crane: Topology of 3-manifolds and conformal field theories. Yale UP 1989 [?]. R. Crowell/R. Fox: Introduction to knot theory. Ginn 1963. M. Culler/C. Gordon/J. Luecke/P. Shalen: Dehn surgery on knots. Annals of Math. 125 (1987), 237-300. David Farmer/Theodore Stanford: Knots and surfaces. AMS 1996, 100p. 0-8218-0451-0. $19. 12154 Jose' Manuel Fernandez de Labastida: Knoten in der Physik. Spektrum 1998/10, 66-72. 5870 M. Fort (ed.): Topology of 3-manifolds. Prentice-Hall 1962. Ralph Fox: Recent developments of knot theory of Princeton. Proc. Int. Congress Math. 2 (1950), 453-457. 5871 Ralph Fox: A quick trip through knot theory. 5870 Fort, 120-176. 5872 Ralph Fox: Knots and periodic transformations. 5870 Fort, 177-182. 5874 Ralph Fox/O. Harrold: The Wilder arcs. 5870 Fort, 184-187. 2241 Peter Freyd a.o.: A new polynomial invariant on knots and links. Bull. AMS 12 (1985), 239-246. [3291] Peter Freyd/D. Yetter: Braided compact closed categories with applications to low dimensional topology. Adv. Math. 77 (1989), 156-182. D. Fuchs: Cohomologies of the braid group mod 2. Funct. Anal. appl. 4 (1970), 143-151. D. Gabai: Foliations and surgery on knots. Bull. AMS 15 (1986), 83-97. N. Gilbert/T. Porter: Knots and surfaces. Oxford UP 1994, 240p. 0-19-853397-7. Pds. 30. "The text is very well written, detailed motivations of concepts and clear explanations replace unnecessary formalism." (Peter Schmitt) 5873 Herman Gluck: The reducibility of embedding problems. 5870 Fort, 182-183. D. Goldschmidt: Group characters, symmetric functions, and the Hecke algebra. AMS 1993, 70p. Pds. 49. "Dieser vorzuegliche Band, dicht gepackt mit Mathematik von allererster Guete, gibt eine Vorlesung wieder, die der Autor 1989 in Berkeley gehalten hat und deren Hauptziel es ist, ein tieferes Verstaendnis der Markovspur und somit des fuer die Knotentheorie so wichtigen Jonespolynoms zu vermitteln." (Harald Rindler). W. Haken: Ueber das Homoeomorphieproblem der 3-Mannigfaltigkeiten I. Math. Zeitschr. 80 (1962), 89-120. V. Hansen: Braids and coverings. Cambridge UP 1989. Geoffrey Hemion: The classification of knots and 3-dimensional spaces. Oxford UP 1992, 160p. 0-19-859697-9. $44. Geoffrey Hemion: On the classification of homeomorphisms of 2-manifolds and the classification of 3-manifolds. Acta Math. 142 (1979), 123-155. F. Jones: Subfactors and knots. AMS 1991, 113p. DM 110. "An enormous amount of material is contained in this short CBMS series of lectures, and what is more, the author is able to link together completely disparate topics such as von Neumann algebras, braid groups, links, and Hecke algebras. Even a superficial perusal of the book will teach something. It belongs on every mathematician's shelf." (G.C. Rota). 6630 Vaughan Jones: Teoria dei nodi e meccanica statistica. 6626 Israel, 27-32. 2240 Vaughan Jones: A polynomial invariant for knots via von Neumann algebras. Bull. AMS 12 (1985), 103-111. [3291] 5877 Vaughan Jones: Hecke algebra representations of braid groups and link polynomials. Annals Math. 126 (1987), 335-388. 4783 Vaughan Jones: Knots in mathematics and physics. 4727 Casacuberta/Castellet, 70-77. 2028 Louis Kauffman: On knots. Princeton UP 1987. Louis Kauffman: Knots and physics. World Scientific 1991, 500p. 981-02-0344-6 (pb). Pds. 19. 5869 Louis Kauffman: Formal knot theory. Princeton UP 1983. 0-691-08336-3. $28. 2234 Louis Kauffman: State models and the Jones polynomial. Topology 26 (1987), 395-407. [3291] Louis Kauffman/S. Lins: Temperley-Lieb recoupling theory and invariants of 3-manifolds. Princeton UP 1994, 300p. 0-691-03640-3 (pb.). $28. 5879 Louis Kauffman/Pierre Vogel: Link polynomials and a graphical calculus. J. Knot Theory and ramif. 1 (1992), 59-104. A. Kawauchi: A survey on knot theory. Birkha''user 1996, 440p. 3-7643-5124-1. SFR 98. 5882 K. Lamotke: Besprechung des Buches "Knots" von Burde/Zieschang. Jber. DMV 90 (1988), B 31-32. 2242 W. Lickorish: Polynomials for links. Bull. London Math. Soc. 20 (1988), 558-588. [3291] W. Lickorish: Prime knots and tangles. Trans. AMS 267 (1981), 321-332. 2775 W. Lickorish: Three-manifolds and the Temperley-Lieb algebra. Math. Annalen 290 (1991), 657-670. W. Lickorish: An introduction to knot theory. Springer 1997, 200p. DM 89. 6283 Charles Livingston: Periodic knots and Maple. Notices AMS 38 (1991), 785-788. Charles Livingston: Knot theory. MAA 1994. C. McCrory/T. Schifrin (ed.): Geometry and topology, varieties and knots. Dekker 1987. 15064 Kishore Marathe: A chapter in physical mathematics - theory of knots in the sciences. In 15031 Engquist/, 873-888. H. Morton: Threading knot diagrams. Math. Proc. Camb. Phil. Soc. 99 (1986), 246-260. 2235 H. Murakami: A formula for the two-variable link polynomial. Topology 26 (1987), 409-412. [3291] K. Murasugi: Knot theory and its applications. Birkha''user 1996, 340p. 3-7643-3817-2. SFR 98. L. Neuwirth: Knot groups. Princeton UP 1965, 110p. 0-691-07991-9. $7. L. Neuwirth (ed.): Knots, groups, and 3-manifolds. Princeton UP 1975. P. Papi/C. Procesi: Invarianti di nodi. Quaderni UMI 1998, 200p. K. Perko: On the classification of knots. Proc. AMS 45 (1974), 262-266. 5878 William Pohl: DNA and differential geometry. Math. Intell. 3 (1980), 20-27. J. Przytycki/P. Traczyk: Invariants of links of Conway type. Kobe J. Math. 4 (1987), 115-139. 6126 K. Rehren: Quantum symmetry associated with braid group statistics. 2853 Doebner/Hennig, 318-339. 2678 K. Reidemeister: Knotentheorie. Chelsea 1948. N. Reshetiken: Quantized universal enveloping algebras, the Yang-Baxter equation, and invariants of links I-II. Steklov Inst. 1987 [?]. 5868 Dale Rolfsen: Knots and links. Publish or Perish 1976. H. Schubert: Bestimmung der Primfaktorzerlegung von Verkettungen. Math. Zeitschrift 76 (1961), 116-148. H. Seifert/W. Threlfall: Old and new results on knots. Can. J. Math. 2 (1950), 1-15. J. Simon: Topological chirality of certain molecules. Topology 25 (1986), 229-235. 14821 Alexei Sossinsky: Mathematik der Knoten. Rowohlt 2000, 160p. DM 17. S. Spengler/A. Stasiak/N. Cozzarelli: The stereostructure of knots and catenanes produced by phage lambda integrative recombination. Implications for mechanism and DNA structure. Cell 42 (1985), 325-334. 12242 Ian Stewart: Katzenkorbknotenknobelei. Spektrum 1999/1, 8-10. Es gibt eine Algebra fu''r Zo''pfe, aber nicht fu''r Fingerfadenfiguren. 5876 John Stillwell: Classical topology and combinatorial group theory. Springer 1980. Chapter 7 deals with knots and braids. 5173 De Witt Sumners: Untangling DNA. Math. Intell. 12/3 (1990), 71-80. De Witt Sumners: Knots, macromolecules and chemical dynamics. In R. King/D. Rouvray (ed.): Graph theory and topology in chemistry. Elsevier 1987, 3-22. De Witt Sumners: The role of knot theory in DNA research. In McCrory/Schifrin, 297-318. 6950 De Witt Sumners: Lifting the curtain. Using topology to probe the hidden action of the enzymes. Notices AMS May 1995, 528-537. D. Walba: Topological stereochemistry. Tetrahedron 41 (1985), 3161-3212. Friedhelm Waldhausen: The word problem in fundamental groups of sufficiently large irreducible 3-manifolds. Annals Math. 88 (1968), 272-280. Solution of the word problem for knot groups. Friedhelm Waldhausen: Recent results on sufficiently large 3-manifolds. Proc. Symp. Pure Math. AMS 32 (1979), 21-37. S. Wasserman/N. Cozzarelli: Biochemical topology. Applications to DNA recombination and replication. Science 232 (1986), 951-960. S. Wasserman/J. Dungan/N. Cozzarelli: Discovery of a predicted DNA knot substantiates a model for site-specific recombination. Science 229 (1985), 171-174. Dominic Welsh: Complexity. Knots, colourings and countings. Cambridge UP 1993, 180p. 0-521-45740-8 (pb). £20. J. White/K. Millett/N. Cozzarelli: Description of the topological entanglement of DNA catenanes and knots by a powerful method involving strand passage and recombination. J. Mol. Biology 197 (1987), 585-603. 2239 E. Witten: Quantum field theory and the Jones polynomial. Comm. Math. Physics 121 (1989), 351-399. [3291] 5875 E. Zeeman: Isotopies and knots in manifolds. 5870 Fort, 187-193.

99. Knot Theory knot theory. knotting index; knot index; alternating knots; Celtic knots; Hyperbolicknot; Intro to knot theory; knots; knot theory; Forensic knot analysis. http://www-math.cudenver.edu/~jstarret/knots.html

Knot Theory A knot is an embedding of S1 in S3 (a 1-sphere in a 3-sphere, or a circle in three space plus the point at infinity), and a link is a disjoint collection of knots. We generally think of a link as being a set of interlocking rings, such as a chain, but here we include unlinked sets, and the rings comprising them can be knotted. A periodic orbit of a continuous time dynamical system with two degrees of freedom is a knot since it is a closed loop embedded in three space. A subset of the set of periodic orbits of a system forms a linkin other words, the periodic orbits may be tangled up with each other in complex and interesting ways. Chaotic dynamical systems are especially interesting from a knot theoretic point of view, as they have an infnite set of unstable periodic orbits that may be tangled in a way that includes every possible type of knot. There are many ways to characterize knots and links that may be used to characterize the orbits of dynamical systems. Among these are the polynomial invariants: Alexander Polynomial Conway Polynomial Jones Polynomial HOMFLYPT Polynomial Suppose we have chaotic time series data from a black box and we want to determine the equations of the underlying dynamics in the box. We may reconstruct the phase space of the experimental system from its time series by the method of time delay embedding and extract the periodic orbits. With a few periodic orbits in hand, we may be able to characterize the dynamics of the system from the polynomial invariants of the knots and links that are the periodic orbits.

100. Quantum Algebra And Topology (Including Knot Theory) Quantum Algebra and Topology (Including knot theory). http//eprints.math.duke.edu/qalg/.Features Web Journal , , - Preprints http://www.aldea.com/guides/ag/a897ud.html

Quantum Algebra and Topology (Including Knot Theory) http://eprints.math.duke.edu/q-alg/ Features: Web Journal , , . Preprints in quantum algebra and topology, beginning November 1994, available in PostScript and various TeX formats. Community Commentary Faculty: Quality ; Quantity ; Ease ; Up-to-date Graduates: Quality ; Quantity ; Ease ; Up-to-date Undergraduates: Quality ; Quantity ; Ease ; Up-to-date Other: Quality ; Quantity ; Ease ; Up-to-date Back to Mathematical sciences Community Commentary Back to UniGuide Academic Guide Site developed and designed by AldeaCommunications For inquiries or to make suggestions email uniguide@aldea.com Last Modified: 8/14/97

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