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Knot:     more books (100)

Unraveling the Integral Knot Concordance Group (Memoirs of the American Mathematical Society) by N.W. Stoltzfus, 1977-12-31 The Branched Cyclic Covering of 2 Bridge Knots and Links (Memoirs of the American Mathematical Society) by Jerome Minkus, 1982-12-31 Differential and Symplectic Topology of Knots and Curves (American Mathematical Society Translations Series 2) by S. Tadachnikoz, 1999-03 Geometric Properties and Problems of Thick Knots (Mathematics Research Developments Series) by Yuanan Diao, Claus Ernst, 2009-12-30 Quantum Field Theory, Statistical Mechanics, Quantum Groups and Topology: Proceedings of the NATO Advanced Research Workshop University of Miami 7-1 by Thomas Curtright, Luca Mezincescu, 1992-10 Knots and Quantum Gravity (Oxford Lecture Series in Mathematics and Its Applications) The Knots Puzzle Book by Heather McLeay, 2000-06 The Classification of Knots and 3-Dimensional Spaces (Oxford Science Publications) by Geoffrey Hemion, 1992-12-01 Knots, Groups and 3-Manifolds: Papers Dedicated to the Memory of R.H. Fox. (AM-84) (Annals of Mathematics Studies) by Lee Paul Neuwirth, 1975-08-01 Knots and Feynman Diagrams by Dirk Kreimer, 2000-07 Quantum Invariants of Knots and 3-Manifolds (De Gruyter Studies in Mathematics) by Vladimir G. Turaev, 2010-04-16 The Geometry and Physics of Knots (Lezioni Lincee) by Michael Atiyah, 1990-10-26 Knots and Links in Three-Dimensional Flows (Lecture Notes in Mathematics) by Robert W. Ghrist, Philip J. Holmes, et all 1997-04-18 Knots and Applications (Series on Knots and Everything)

lists with details

81. PHYSICAL AND NUMERICAL MODELS IN KNOT THEORY
    PHYSICAL AND NUMERICAL MODELS IN knot theory. Together, the chapters explore four major themes physical knot theory, knot theory in the life sciences,  
    http://www.worldscibooks.com/mathematics/5766.html
    
    Extractions: The physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year. This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration of spaces of knots, knotted umbilical cords, studies of knots in DNA and proteins, and the structure of tight knots. Together, the chapters explore four major themes: physical knot theory, knot theory in the life sciences, computational knot theory, and geometric knot theory.

82. FUNCTORIAL KNOT THEORY
    FUNCTORIAL knot theory. All the definitions from both knot theory and category theory are included, as well as proofs of many basic results which are  
    http://www.worldscibooks.com/mathematics/4542.html
    
    Extractions: Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory. This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low-dimensional topology. The focus then turns to the deformation theory of monoidal categories and the related deformation theory of monoidal functors, which is a proper generalization of Gerstenhaber's deformation theory of associative algebras. These serve as the building blocks for a deformation theory of braided monoidal categories which gives rise to sequences of Vassiliev invariants of framed links, and clarify their interrelations.

83. Knot Theory
    Maths knot theory. knot theory is a branch of mathematics dealing with tangled loops. When there s just one loop, it s called a knot.  
    http://f2.org/maths/kt/
    
    Extractions: Up to Home Maths Site Map Text version 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 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

84. Knot Theory History
    History. This web site is for the basic understanding of where knot theory came from. The history of knot theory began in the very early 1800 s.  
    http://www.kpbsd.k12.ak.us/kchs/JimDavis/CalculusWeb/Knot Theory History.htm
    
    Extractions: Knot Theory History This web site is for the basic understanding of where Knot Theory came from. Johann Frederich Carl Gauss (1775-1855) The history of Knot Theory began in the very early 1800's. Johann Frederich Carl Gauss was a German mathematician who was interested in the idea of knots. His contribution to the Knot Theory was "analysis situs." Analysis situs deals with the mathematical differences between the simple and complex knots. The mathematical differences are very different to the human eye, but until then, they were difficult to distinguish them mathematically. Lord Kelvin, William Thomson (1824-1907) Until the late 1800's no one was really interested in the idea of knots. Lord Kelvin, also known as William Thomson, was an English scientist who taught at the University of Glasgow. One of his greatest achievements was the idea of "ether." His belief was that the universe was filled with an invisible and frictionless fluid called "ether," and the atoms were the vortices in this fluid in the shape of knots. Thus a table of knots would be a table of elements. This of course was later on disproved when atomic ideas began to emerge. The Knot Theory soon faded away until the 1950's. James Watson (left) and Francis Crick (right) The race to discover the shape of deoxyribonucleic acid (DNA) was all over the world. When it was finally finish, the idea of knots came back to life. In 1953, James Watson and Francis Crick discovered that DNA was in the shape of a double helix. This concept led to discovering that DNA had parts of it knotted in many locations. With the help of both of these scientists, Knot Theory came back with scientist thinking up new ideas fighting diseases and understanding the make-up of all living things.

85. Louis H. Kauffman
    I am a topologist working in knot theory and its relationships with statistical KNOTS A short course in knot theory from Reidemeister moves to state  
    http://www.math.uic.edu/~kauffman/
    
    Extractions: Louis H. Kauffman I am teaching Calculus, Math 180 in Fall 2005. See Calculus. I taught Applied Linear Algebra, Math 310 in Spring 2005. See Vector Algebra. I taught Calculus, Math 181 in Spring 2005. See Calculus. In July 2004 I taught a workshop on knots and applications at the MSRI workshop at University of British Columbia in Vancouver, BC. See Knots in Vancouver for a course description and for downloads for the course. I visited from September 1, 2003 to August 31, 2004 at the University of Waterloo and the Perimeter Institute in Waterloo, Canada. In the winter term I taught a course on knots and physics at the university. See

86. Math 486-S Knot Theory
    Math 486S knot theory At Left Photo of Gordian Knot by sculptor John Robinson, the creator of many mathematically-themed artworks.  
    http://web.library.emory.edu/subjects/science/math/486-S.html
    
    Extractions: Table Of Contents At Left: Photo of " Gordian Knot " by sculptor John Robinson, the creator of many mathematically-themed artworks . His " Immortality " is a Möbius band in a trefoil knot. Getting Started top Knot theory , the mathematical study of knots, is part of a branch of mathematics called topology (the definitions linked here are from MathWorld ). It has applications in chemistry, biology, and physics. It is almost paradoxical that while many questions in knot theory are simple to state and easy to understand, the solutions to those questions can require a deep and intricate understanding of higher mathematics.

87. Syllabus For Topics In Geometry & Topology: Knot Theory, Fall 2003
    Supplementary Texts The Knot Book by Adams and knot theory Its Applications by Murasugi. Requirements We will assume familiarity with linear algebra and  
    http://www.math.columbia.edu/~ikofman/knotsyllabus.html
    
    Extractions: Web site: http://www.math.columbia.edu/~ikofman/ Course Time and Place: 2:40pm - 3:55pm Tuesday and Thursday, 520 Mathematics Building Text: Knots, Links, Braids and 3-Manifolds: An Introduction to the New Invariants in Low-Dimensional Topology by Prasolov and Sossinsky Supplementary Texts: The Knot Book by Adams and by Murasugi Requirements: We will assume familiarity with linear algebra and some group theory. Basic Topology is not required, though it provides a useful perspective for knot theory. You will be asked to think about mathematical ideas and to prove what you think is true, so a certain amount of mathematical maturity is expected. Material Covered: Basics of knots, links, and their diagrams, elementary knot invariants, Jones-type polynomials, Vassiliev invariants, braids, Seifert matrices and Alexander polynomial, 3-manifold topology, including Heegaard diagrams, surgery, and branched covers of knots. Homework: Assignments will be announced in class and then posted on this website. Any changes will be announced in class. Incomplete work with good progress will be rewarded.

88. Knot Theory: Information From Answers.com
    knot theory Trefoil knot, the simplest nontrivial knot. knot theory is a branch of topology that was inspired by observations, as the name suggests,  
    http://www.answers.com/topic/knot-theory
    
    Extractions: showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Best of Web Mentioned In Or search: - The Web - Images - News - Blogs - Shopping knot theory Wikipedia knot theory Trefoil knot, the simplest non-trivial knot. Knot theory is a branch of topology that was inspired by observations, as the name suggests, of knots . But progress in the field no longer depends on experiments with twine. Knot theory concerns itself with abstract properties of theoretical knots In mathematical jargon , knots are embeddings of the closed circle in three-dimensional space. An ordinary knot is converted to a mathematical knot by splicing its ends together. The topological theory of knots asks whether two such knots can be rearranged to match, without opening the splice. The question of untying an ordinary knot has to do with unwedging tangles of rope pulled tight. A knot can be untied in the topological theory of knots if and only if it is equivalent to the unknot , a circle in 3-space. Knot theory originated in an idea of Lord Kelvin 's (1867), that atoms were knots of swirling vortices in the

89. QA Quantum Algebra
    Key College Publishing Why Knot? An Introduction to the knot theory! “Why Knot? is a witty, lighthearted exploration of a topic of knot theory is appealing and accessible it naturally lends itself to lots  
    http://eprints.math.duke.edu/archive/q-alg

90. A Family Of Impossible Figures Studied By Knot Theory
    studied by knot theory. Corinne Cerf. Mathematics Dept., CP 216. Université Libre de Bruxelles. B1050 Bruxelles, Belgium. ccerf@ulb.ac.be. 1. Introduction  
    http://www.mi.sanu.ac.yu/vismath/cerf/
    
    Extractions: 1. Introduction Impossible figures are fascinating objects, related to art, psychology, and mathematics [ ]. Lionel and Roger Penrose (father and son) introduced the impossible tribar in 1958 [ Fig. 1 ). A figure is called impossible when "a contradiction in our interpretation is noticed but does not result in our rejecting it in favour of a consistent one" [ ]. The object represented in Fig. 1 is an impossible figure because our mind tries to interpret it as a three-dimensional (3D) object in the Euclidean space, with straight edges and planar faces, instead of interpreting it, for example, as a two-dimensional object drawn on the paper plane (which is perfectly possible). Fig. 1 Impossible figures have inspired researchers with more than one hundred papers (see Kulpa [ ] for an extensive bibliography), and the Dutch artist Escher [ ] with some famous drawings (see e.g. Fig. 2

91. Differential Geometry And Knot Theory
    Differential Geometry and knot theory. The knot theory part of the course is concerned with various ways to embed a circle in Euclidean space and how  
    http://www.ma.umist.ac.uk/kd/ma351/ma351.html
    
    Extractions: General description: The differential geometry part of this course involves the study of curves and surfaces in three-dimensional Euclidean space. Using vector calculus and moving frames of reference on curves embedded in surfaces we can define quantities such as Gaussian curvature that allow us to distinguish among surfaces. The knot theory part of the course is concerned with various ways to embed a circle in Euclidean space and how two knots can be distinguished from one another.

92. NSF Knot Theory Grant
    knot theory for Preservice and Practicing Secondary Mathematics Teachers NSF DUE Award 0126685. Principal Investigators. Neil Portnoy Thomas W. Mattman  
    http://www.csuchico.edu/math/mattman/NSF.html

93. Knot Theory Links
    knot theory for Teachers. http//www.csuchico.edu/math/mattman/NSF.html A knot theory Primer. http//www.inst.bnl.gov/~wei/contents.html  
    http://www.csuchico.edu/math/mattman/NSF/Links.html

94. Knot Theory (190) Course, Fall 2003
    With a little care we can do quite a lot of knot theory without needing to talk about the If you get really interested in knot theory and want a less  
    http://www.math.ucsd.edu/~justin/190.html
    
    Extractions: The traditional first course in topology deals with ``point-set topology'': the study of metric and topological spaces, continuity, compactness, connectedness, and other properties beginning with ``c''. This branch of the subject is really just a part of analysis, and while it is important for the foundations of the subject and can help you learn to write proofs properly, it can all seem very abstract and dry. Where are the doughnuts, coffee cups, pretzels, rubber sheets, knots and so on of popular topology? Traditionally, we teach the more geometric, visual side of the subject after teaching all the basic tools. This is not unreasonable, but it does take a long time to do properly, and is quite hard to motivate because it turns history on its head. After all, people have been using and thinking about knots for thousands of years, but the definition of a topological space is only a hundred years old. Fortunately it isn't necessary to work this way round. With a little care we can do quite a lot of knot theory without needing to talk about the foundational aspects of topology. I intend to start this way, and then try to develop a little bit of the abstract theory only if we really start to need it later on.

95. Open Problems In Knot Theory
    A List of Approachable Open Problems in knot theory Suggested by Colin Adams during the knot theory Workshop at Wake Forest University during June 2428  
    http://www.williams.edu/Mathematics/cadams/knotproblems.html
    
    Extractions: .ps and .pdf files also available) What knots with high symmetries have projections that demonstrate this symmetry? (eg. the Figure-8 knot) Find specific families of knots satisfying the property c(K_1#K_2) = c(K_1)+c(K_2), where c=c(K) is the crossing number and # means knot composition. (eg. This is known for alternating knots.) What about torus knots? [In a 2003 preprint, Yuanan Diao demonstrated that this does hold for compositions of torus knots, as well. This was also independently proved by Herman Gruber. His paper is available at arxiv.org under math.GT/0303273.] When is a knot equivalent to its inverse? (The inverse has the same projection but with an opposite orientation). (eg. the trefoil and its inverse) Hass and Lagrias proved that if you have an n-crossing projection of the trivial knot, you can turn it into a trivial projection by using no more than 2^(1,000,000,000n) Reidemeister moves. Find a better upper bound. Find a pair of non-tricolorable knots whose composition istricolorable or show that this is not possible. (To show it's false, it's enough to show that an open knot is tricolorable if and only if its closure is tricolorable.)

96. Knot Theory
    Find It Science Math Topology knot theory Sections on knot tying, mathematical knot theory, knot art, and knot books.  
    http://www.ebroadcast.com.au/dir/Science/Math/Topology/Knot_Theory/

97. Knot Theory With KnotPlot
    knot theory with KnotPlot. Equilateral Stick Numbers. This research is in collaboration with Eric Rawdon of the Department of Mathematics at Duquesne  
    http://www.colab.sfu.ca/KnotPlot/ktheory.html
    
    Extractions: This research is in collaboration with Eric Rawdon of the Department of Mathematics at Duquesne University in Pittsburgh. We've used KnotPlot to find equilateral polygonal representatives of all knots to 10 crossings with the fewest number of sides. This number of sides is known as the equilateral stick number. It can be compared to the stick number, which is the same quantity when the constraint of being equilateral is dropped. Surprisingly, for 242 of the 249 prime knots examined, all have an equilateral stick number equal to their stick numbers. Title: Upper Bounds for Equilateral Stick Numbers Authors: Eric J. Rawdon and Robert G. Scharein Abstract: We use algorithms in the software KnotPlot to compute upper bounds for the equilateral stick numbers of all prime knots through 10 crossings, i.e. the least number of equal length line segments it takes to construct a conformation of each knot type. We find seven knots for which we cannot construct an equilateral conformation with the same number of edges as a minimal non-equilateral conformation, notably the 8 knot.

98. Alexa - Browse: Knot Theory
    Alexa web search a new kind of search engine. With traffic rankings, user reviews and other information about sites, Alexa is a web site discovery tool.  
    http://www.alexa.com/browse?&CategoryID=26948

99. Knot Theory -- Facts, Info, And Encyclopedia Article
    knot theory is a branch of (The configuration of a communication network) knot theory concerns itself with abstract properties of (Click link for more  
    http://www.absoluteastronomy.com/encyclopedia/k/kn/knot_theory.htm
    
    Extractions: Knot theory is a branch of (The configuration of a communication network) topology that was inspired by observations, as the name suggests, of (Any of various fastenings formed by looping and tying a rope (or cord) upon itself or to another rope or to another object) knot s. But progress in the field no longer depends on experiments with twine. Knot theory concerns itself with abstract properties of (Click link for more info and facts about theoretical knots) theoretical knots In (Click link for more info and facts about mathematical) mathematical (Specialized technical terminology characteristic of a particular subject) jargon , knots are (Click link for more info and facts about embedding) embedding s of the closed circle in three-dimensional space. An ordinary knot is converted to a mathematical knot by splicing its ends together. The topological theory of knots asks whether two such knots can be rearranged to match, without opening the splice. The question of untying an ordinary knot has to do with unwedging tangles of rope pulled tight. A knot can be untied in the topological theory of knots if and only if it is equivalent to the unknot , a circle in 3-space.

100. [math/0411115] Knot Theory Of Complex Plane Curves
     knot theory of complex plane curves. Authors Lee Rudolph Comments 26 figures; to appear in Handbook of knot theory (W. Menasco and M. Thistlethwaite, eds.  
     http://arxiv.org/abs/math.GT/0411115
     
     Extractions: The primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally oriented. There are many natural classes of examples: links of singularities; links at infinity; links of divides, free divides, tree divides, and graph divides; andmost generallyquasipositive links. Totally tangential C-links are unoriented but naturally framed; they turn out to be precisely the real-analytic Legendrian links, and can profitably be investigated in terms of certain closely associated transverse C-links. The knot theory of complex plane curves is attractive not only for its own internal results, but also for its intriguing relationships and interesting contributions elsewhere in mathematics. Within low-dimensional topology, related subjects include braids, concordance, polynomial invariants, contact geometry, fibered links and open books, and Lefschetz pencils. Within low-dimensional algebraic and analytic geometry, related subjects include embeddings and injections of the complex line in the complex plane, line arrangements, Stein surfaces, and Hilbert's 16th problem.

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