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Knot: more books (100)

Knot Theory by Charles Livingston, 1993-01-01
Knot Theory and Its Applications by Kunio Murasugi, 1998
Virtual Knot Theory (an introduction to the theory of virtual knots) by LOUIS H. KAUFFMAN, 1999
Knot Theory
Introduction to Knot Theory
Proceedings of the International Conference on Knot Theory and Related Topics
The Mathematics of Knots: Theory and Application (Contributions in Mathematical and Computational Sciences)
Knots (De Gruyter studies in mathematics) by Gerhard Burde, 1985
Tied up in knots: anything that can tangle up, will, including DNA.: An article from: Science News by Davide Castelvecchi, 2007-12-22
Classical Circuit Theory by Omar Wing, 2008-10-06
A Frayed Knot by Felix Culp, 2010-08-05
Lectures at Knots '96: International Conference Center, Waseda Univ., Tokyo 22-31 July 1996 (Series on Knots and Everything)
Gauss Diagram Invariants for Knots and Links (Mathematics and Its Applications) by T. Fiedler, 2001-08-01
Knots and Surfaces by N. D. Gilbert, T. Porter, et all 1994-01-15

lists with details

Is String Theory In Knots?
This essay is an incomplete attempt to formulate the equations for an algebraic theory of gravity in terms of knot relations.
http://adela.karlin.mff.cuni.cz/~motl/Gibbs/knots.htm

Extractions: Is String Theory in Knots? Surely Not Knots When I was a mathematics student at Cambridge back in 1980, I remember going to one of John Conway's popular lectures which he gave to the mathematics clubs. This one was about knot theory. Conway performed a series of tricks with bits of rope to demonstrate various properties of knots. A fundamental unsolved problem in knot theory, he told us, is to discover an algorithm which can tell when a loop of string is a knot or not. It is possible to tie up closed loops of string into complicated tangles which can nevertheless be untied without cutting the string. But suppose I gave you a tangled loop of string. How could you determine if it could be untied? Conway showed us a clever trick with groups which enabled him to determine that some knotted loops could not be untied, but there were others which were not classified in this way. Conway had generalised a polynomial invariant of knots first discovered by Alexandria many years ago. The Conway Polynomial was quite a powerful tool to distinguish some knots from others, but it could not separate all. I remember thinking at the time that this was a piece of pure maths which would never have any useful applications apart from providing a way of proving that your boat can't slip its moorings, perhaps. Mathematicians delight in these kind of problems.
The KnotPlot Site
The KnotPlot Site, a visual exploration of mathematical knots. my thesis; Short discussion on braid theory (incomplete) and a few neat pretzel knots
http://www.cs.ubc.ca/nest/imager/contributions/scharein/KnotPlot.html

Extractions: Here you will find a collection of knots and links, viewed from a (mostly) mathematical perspective. Nearly all of the images here were created with KnotPlot, a fairly elaborate program to visualize and manipulate mathematical knots in three and four dimensions. You can download KnotPlot and try it on your computer (see the link below), but first you may want to look at some of the images in the picture gallery. Also, have a browse through the Guestbook or sign it yourself Check out the mathematical knots M ) page as well to see more knot pictures. Or try some of the following examples to see some knots in a different light. The pages marked with have been updated or created as of 11 Feb 2003. Those marked with an M have at least one MPEG animation. The KnotServer (experimental, still not too useful), : 3D interactive viewer (which can save 3D models). Knots as radiating tubes M More knots as radiating tubes Decorative knots: on white on black goth Fancy Knots and Links,
Untangling The Mathematics Of Knots
Knots have been studied extensively by mathematicians for the last hundred years. Recently the study of knots has proved to be of great interest to
http://www.c3.lanl.gov/mega-math/workbk/knot/knot.html

Extractions: Knots have been studied extensively by mathematicians for the last hundred years. Recently the study of knots has proved to be of great interest to theoretical physicists and molecular biologists. One of the most peculiar things which emerges as you study knots is how a category of objects as simple as a knot could be so rich in profound mathematical connections. Here are a variety of activities for exploring knots made from pieces of rope. Students can make and verify observations about knots, classify them, combine them, and find ways to determine if two knots are alike. The activities outlined here can be combined to form a single lesson about mathematical knots, or a larger investigative unit that extends over a longer period of time. The sequence in which the activities are listed is roughly in order of increasing difficulty and challenge, but all of the earlier activities are not strict prerequisites for the later ones. Finding ways to make precise spoken or written statements about an inherently spatial and manipulative experience is a meaningful and interesting challenge for all students. Teachers can help students learn to do this by helping them develop classroom conventions for naming knots, parts of knots, groups of knots, or for labeling parts of knots to make them easier to talk about. Although presentations and discussions are appropriate as a whole-class activity when studying knots, most of these activities will work best when students work individually, in pairs and small groups. It is important for each stu dent to be able touch and twist the knots that they are thinking about.
Research Group On Topological Quantum Field Theory And Knots
Research Group on Topological Quantum Field Theories in any dimension and their relation to topological invariants. Particular attention is given to BF theories and knots in any dimension.
http://wwwteor.mi.infn.it/users/cotta/tqft.html

Extractions: Research Group on Topological Quantum Field Theories and Knots Goals To study topological field theories in any dimension and their relation to topological invariants. Particular attention is given to BF theories. Topological invariants include 3-manifold invariants and invariants of ordinary links and knots and, at the higher dimensional level, the homology and cohomology of the spaces of imbedded and immersed loops and spheres. Participants Alberto Cattaneo Assistant Professor of Mathematics, University of Zurich, Switzerland asc@math.unizh.ch Paolo Cotta-Ramusino paolo.cotta@mi.infn.it Riccardo Longoni ... riccardo.longoni@mi.infn.it Maurizio Rinaldi rinaldi@univ.trieste.it Carlo Rossi PhD Student in Mathematics, University of Zurich, Switzerland carossi@math.unizh.ch Preprints and recent publications A. S. Cattaneo,
Topology Of Plane Curves, Wave Fronts, Legendrian Knots, Sturm Theory And Flatte
Topology of Plane Curves, Wave Fronts, Legendrian Knots, Sturm theory and Flattenings of Projective Curves. VI Arnold. The theory of smooth (possibly
http://www.mathunion.org/Publications/Bulletins/39/Arnold.html

Extractions: V.I. Arnold The theory of smooth (possibly selfintersecting) curves in the plane is parallel to knot theory (the last being a simplified, commutative version of the theory of plane curves). Strangely, the theory of plane curves invariants has not been developed until 1992, when the simplest three basic invariants (the "strangeness" St, counting the triple points crossings, and the "tangencies crossings counting" invariants J+ and J-) have been introduced, motivated by the symplectic and contact topology problems. In a sense these invariants are similar to the Vassiliev invariants of knot theory. Recently Viro has discovered their relation to the real algebraic geometry, then Schumakovich and Polyak have found the expressions of these new invariants in the spirit of the statistical physics and have related them to the Vassiliev knot invariants, while Lin and Wang have described their relations to the quantum field theory and to the Kontsevich and Bar Natan works on integral formulas for the knot invariants. In spite of the fast progress of the last two years in this domain (including the Aicardi's and Polyak's extension of the theory to the wave fronts, that is to the curves with cusps), the original problems, triggering all the theory, remain unsolved : these problems belong to the symplectic and contact topology of the Lagrangian and Legendrian mappings.
Page Personnelle : Christine Lescop
Directrice de recherches Institut Fourier, UMR 5582 du CNRS Université de Grenoble I BP 74, 38402 SaintMartin d Hères cedex, France
http://www-fourier.ujf-grenoble.fr/~lescop/

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