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Knot Theory

Author: Vassily Olegovich Manturov

Publisher: CRC Press

Published: 2004-02-24

Total Pages: 417

ISBN-13: 0203402847

Since discovery of the Jones polynomial, knot theory has enjoyed a virtual explosion of important results and now plays a significant role in modern mathematics. In a unique presentation with contents not found in any other monograph, Knot Theory describes, with full proofs, the main concepts and the latest investigations in the field. The book is divided into six thematic sections. The first part discusses "pre-Vassiliev" knot theory, from knot arithmetics through the Jones polynomial and the famous Kauffman-Murasugi theorem. The second part explores braid theory, including braids in different spaces and simple word recognition algorithms. A section devoted to the Vassiliev knot invariants follows, wherein the author proves that Vassiliev invariants are stronger than all polynomial invariants and introduces Bar-Natan's theory on Lie algebra respresentations and knots. The fourth part describes a new way, proposed by the author, to encode knots by d-diagrams. This method allows the encoding of topological objects by words in a finite alphabet. Part Five delves into virtual knot theory and virtualizations of knot and link invariants. This section includes the author's own important results regarding new invariants of virtual knots. The book concludes with an introduction to knots in 3-manifolds and Legendrian knots and links, including Chekanov's differential graded algebra (DGA) construction. Knot Theory is notable not only for its expert presentation of knot theory's state of the art but also for its accessibility. It is valuable as a professional reference and will serve equally well as a text for a course on knot theory.

Modeling Time-Varying Unconditional Variance by Means of a Free-Knot Spline-GARCH Model

Author: Oliver Old

Publisher: Springer Nature

Published: 2022-07-27

Total Pages: 260

ISBN-13: 3658386185

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The book addresses the problem of a time-varying unconditional variance of return processes utilizing a spline function. The knots of the spline functions are estimated as free parameters within a joined estimation process together with the parameters of the mean, the conditional variance and the spline function. With the help of this method, the knots are placed in regions where the unconditional variance is not smooth. The results are tested within an extensive simulation study and an empirical study employing the S&P500 index.

A Summary of Modulus of Elasticity and Knot Size Surveys for Laminating Grades of Lumber

Author: R. W. Wolfe

Publisher:

Published: 1981

Total Pages: 24

ISBN-13:

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The Mystery of Knots

Author: Charilaos N. Aneziris

Publisher: World Scientific

Published: 1999

Total Pages: 410

ISBN-13: 9810238789

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One of the most significant unsolved problems in mathematics is the complete classification of knots. The main purpose of this book is to introduce the reader to the use of computer programming to obtain the table of knots. The author presents this problem as clearly and methodically as possible, starting from the very basics. Mathematical ideas and concepts are extensively discussed, and no advanced background is required.

Geoff Wilson's Fishing Knots & Rigs

Author: Geoff Wilson

Publisher: Australian Fishing Network

Published: 2011

Total Pages: 72

ISBN-13: 9781865131849

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Book & DVD. Geoff has been tying and testing fishing knots for over forty years and his knowledge in this field is second to none. This Special Edition of his world-wide best selling book comes in an instructional / interactive book / DVD format featuring Geoff tying his own preferred knots and rigs. Running over 144 minutes, the DVD covers how to tie knots in clear and precise detail. As we all know, the best way to learn how to tie a knot is to actually see it done! This book will be an instant best seller and is attractively presented in a hard cover edition, ideal as a gift for the discerning angler wanting to expand their fishing knowledge.

Topics in Knot Theory

Author: M.E. Bozhüyük

Publisher: Springer Science & Business Media

Published: 1993-08-31

Total Pages: 378

ISBN-13: 9780792322856

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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.

Knots & Splices

Author: Cyrus L. Day

Publisher: Bloomsbury Publishing USA

Published: 2006-06-20

Total Pages: 65

ISBN-13: 0071474668

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This is a pocket-sized book on rope and wire work, splices, knots and rope work. Fully illustrated.

The Book of Knots

Author: Geoffrey Budworth

Publisher: Ivy Press

Published: 2021-07-13

Total Pages: 178

ISBN-13: 0711257426

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The fundamental skill of tying knots is useful in countless situations, both indoors and out. The Book of Knots teaches you which knot to choose and exactly how to tie it, whether you’re constructing a trout fly, repairing a hammock, mooring a boat, securing a load to a car roof rack, or engaging in a rescue or survival situation. This invaluable manual explains through clear line diagrams and step-by-step descriptions how to tie more than 125 practical knots.

Virtual Knots

Author: Vasilii Olegovich Manturov

Publisher: World Scientific

Published: 2012

Total Pages: 553

ISBN-13: 9814401137

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The book is the first systematic research completely devoted to a comprehensive study of virtual knots and classical knots as its integral part. The book is self-contained and contains up-to-date exposition of the key aspects of virtual (and classical) knot theory.Virtual knots were discovered by Louis Kauffman in 1996. When virtual knot theory arose, it became clear that classical knot theory was a small integral part of a larger theory, and studying properties of virtual knots helped one understand better some aspects of classical knot theory and encouraged the study of further problems. Virtual knot theory finds its applications in classical knot theory. Virtual knot theory occupies an intermediate position between the theory of knots in arbitrary three-manifold and classical knot theory.In this book we present the latest achievements in virtual knot theory including Khovanov homology theory and parity theory due to V O Manturov and graph-link theory due to both authors. By means of parity, one can construct functorial mappings from knots to knots, filtrations on the space of knots, refine many invariants and prove minimality of many series of knot diagrams.Graph-links can be treated as OC diagramless knot theoryOCO: such OC linksOCO have crossings, but they do not have arcs connecting these crossings. It turns out, however, that to graph-links one can extend many methods of classical and virtual knot theories, in particular, the Khovanov homology and the parity theory.

Lunda Geometry: Mirror Curves, Designs, Knots, Polyominoes, Patterns, Symmetries

Author: Paulus Gerdes

Publisher: Lulu.com

Published: 2008-06-26

Total Pages: 204

ISBN-13: 1435726294

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The book "Lunda Geometry" explains how the mathematical concepts of mirror curves and Lunda-designs were discovered in the context of the author's research of 'sona', illustrations traditionally made in the sand by Cokwe storytellers from eastern Angola (a region called Lunda) and neighboring regions of Congo and Zambia. Examples of mirror curves from several cultures are presented. Lunda-designs are aesthetically attractive and display interesting symmetry properties. Examples of Lunda-patterns and Lunda-polyominoes are presented. Some generalizations of the concept of Lunda-design are discussed, like hexagonal Lunda-designs, Lunda-k-designs, Lunda-fractals, and circular Lunda-designs. Lunda-designs of Celtic knot designs are constructed.Several chapters were published in journals like 'Computers & Graphics' (Oxford), 'Visual Mathematics' (Belgrade), and 'Mathematics in School' (UK).