Linknot Knot Theory By Computer PDF Download
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| Author | : Slavik V. Jablan |
| Publisher | : World Scientific |
| Total Pages | : 497 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 9812772235 |
Download LinKnot Book in PDF, ePub and Kindle
LinKnot - Knot Theory by Computer provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics. The book covers basic notions in knot theory, as well as new methods for handling open problems such as unknotting number, braid family representatives, invertibility, amphicheirality, undetectability, non-algebraic tangles, polyhedral links, and (2,2)-moves. Conjectures discussed in the book are explained at length. The beauty, universality and diversity of knot theory is illuminated through various non-standard applications: mirror curves, fullerens, self-referential systems, and KL automata.
| Author | : Slavik Vlado Jablan |
| Publisher | : World Scientific |
| Total Pages | : 497 |
| Release | : 2007-11-16 |
| Genre | : Mathematics |
| ISBN | : 9814474037 |
Download Linknot: Knot Theory By Computer Book in PDF, ePub and Kindle
LinKnot — Knot Theory by Computer provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics.The book covers basic notions in knot theory, as well as new methods for handling open problems such as unknotting number, braid family representatives, invertibility, amphicheirality, undetectability, non-algebraic tangles, polyhedral links, and (2,2)-moves.Hands-on computations using Mathematica or the webMathematica package LinKnot and beautiful illustrations facilitate better learning and understanding. LinKnot is also a powerful research tool for experimental mathematics implementation of Caudron's ideas. The use of Conway notation enables experimenting with large families of knots and links.Conjectures discussed in the book are explained at length. The beauty, universality and diversity of knot theory is illuminated through various non-standard applications: mirror curves, fullerens, self-referential systems, and KL automata.
| Author | : Charilaos N. Aneziris |
| Publisher | : World Scientific |
| Total Pages | : 410 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 9810238789 |
Download The Mystery of Knots Book in PDF, ePub and Kindle
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.
| Author | : M.E. Bozhüyük |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 355 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401116954 |
Download Topics in Knot Theory Book in PDF, ePub and Kindle
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.
| Author | : S. Moran |
| Publisher | : Elsevier |
| Total Pages | : 309 |
| Release | : 2000-04-01 |
| Genre | : Computers |
| ISBN | : 0080871933 |
Download The Mathematical Theory of Knots and Braids Book in PDF, ePub and Kindle
This book is an introduction to the theory of knots via the theory of braids, which attempts to be complete in a number of ways. Some knowledge of Topology is assumed. Necessary Group Theory and further necessary Topology are given in the book. The exposition is intended to enable an interested reader to learn the basics of the subject. Emphasis is placed on covering the theory in an algebraic way. The work includes quite a number of worked examples. The latter part of the book is devoted to previously unpublished material.
| Author | : Louis H. Kauffman |
| Publisher | : World Scientific |
| Total Pages | : 577 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 9814313009 |
Download Introductory Lectures on Knot Theory Book in PDF, ePub and Kindle
More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.
| Author | : Kunio Murasugi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 348 |
| Release | : 2009-12-29 |
| Genre | : Mathematics |
| ISBN | : 0817647198 |
Download Knot Theory and Its Applications Book in PDF, ePub and Kindle
This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as 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. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.
| Author | : Vassily Olegovich Manturov |
| Publisher | : CRC Press |
| Total Pages | : 507 |
| Release | : 2018-04-17 |
| Genre | : Mathematics |
| ISBN | : 1351359126 |
Download Knot Theory Book in PDF, ePub and Kindle
Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text. Knot Theory, Second Edition 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 profes-sional reference and will serve equally well as a text for a course on knot theory.
| Author | : Tomotada Ohtsuki |
| Publisher | : World Scientific |
| Total Pages | : 516 |
| Release | : 2002 |
| Genre | : Invariants |
| ISBN | : 9789812811172 |
Download Quantum Invariants Book in PDF, ePub and Kindle
This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The ChernOCoSimons field theory and the WessOCoZuminoOCoWitten model are described as the physical background of the invariants. Contents: Knots and Polynomial Invariants; Braids and Representations of the Braid Groups; Operator Invariants of Tangles via Sliced Diagrams; Ribbon Hopf Algebras and Invariants of Links; Monodromy Representations of the Braid Groups Derived from the KnizhnikOCoZamolodchikov Equation; The Kontsevich Invariant; Vassiliev Invariants; Quantum Invariants of 3-Manifolds; Perturbative Invariants of Knots and 3-Manifolds; The LMO Invariant; Finite Type Invariants of Integral Homology 3-Spheres. Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics."
| Author | : Charles Livingston |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 240 |
| Release | : 1993-12-31 |
| Genre | : Knot theory |
| ISBN | : 1614440239 |
Download Knot Theory Book in PDF, ePub and Kindle
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. Livingston guides readers through a general survey of the topic showing how to use the techniques of linear algebra to address some sophisticated problems, including one of mathematics's 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.
