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New Developments In The Theory Of Knots

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New Developments In The Theory Of Knots

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Author : Toshitake Kohno
language : en
Publisher: World Scientific
Release Date : 1990

New Developments In The Theory Of Knots written by Toshitake Kohno and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

This reprint volume focuses on recent developments in knot theory arising from mathematical physics, especially solvable lattice models, Yang-Baxter equation, quantum group and two dimensional conformal field theory. This volume is helpful to topologists and mathematical physicists because existing articles are scattered in journals of many different domains including Mathematics and Physics. This volume will give an excellent perspective on these new developments in Topology inspired by mathematical physics.

New Developments In The Theory Of Knots

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Author : Toshitake Kohno
language : en
Publisher: World Scientific
Release Date : 1990-08-31

Linknot

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Author : Slavik V. Jablan
language : en
Publisher: World Scientific
Release Date : 2007

Linknot written by Slavik V. Jablan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

LinKnot OCo 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 (available online at http: //math.ict.edu.rs ) 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. Sample Chapter(s). 1.1 Basic graph theory (176 KB). Contents: Notation of Knots and Links; Recognition and Generation of Knots and Links; History of Knot Theory and Applications of Knots and Links. Readership: Researchers interested in knot theory and users of Mathematica."

Introductory Lectures On Knot Theory

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Author : Louis H. Kauffman
language : en
Publisher: World Scientific
Release Date : 2012

Introductory Lectures On Knot Theory written by Louis H. Kauffman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

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.

New Developments In The Theory Of Knots

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Author : Toshitake Kohno
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 1990

New Developments In The Theory Of Knots written by Toshitake Kohno and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

An Introduction To Knot Theory

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Author : W.B.Raymond Lickorish
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

An Introduction To Knot Theory written by W.B.Raymond Lickorish and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This account is an introduction to mathematical knot theory, the theory of knots and links of simple closed curves in three-dimensional space. Knots can be studied at many levels and from many points of view. They can be admired as artifacts of the decorative arts and crafts, or viewed as accessible intimations of a geometrical sophistication that may never be attained. The study of knots can be given some motivation in terms of applications in molecular biology or by reference to paral lels in equilibrium statistical mechanics or quantum field theory. Here, however, knot theory is considered as part of geometric topology. Motivation for such a topological study of knots is meant to come from a curiosity to know how the ge ometry of three-dimensional space can be explored by knotting phenomena using precise mathematics. The aim will be to find invariants that distinguish knots, to investigate geometric properties of knots and to see something of the way they interact with more adventurous three-dimensional topology. The book is based on an expanded version of notes for a course for recent graduates in mathematics given at the University of Cambridge; it is intended for others with a similar level of mathematical understanding. In particular, a knowledge of the very basic ideas of the fundamental group and of a simple homology theory is assumed; it is, after all, more important to know about those topics than about the intricacies of knot theory.

New Developments In The Theory Of Knots

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Author : Toshitake Kohno
language : en
Publisher:
Release Date : 1989

New Developments In The Theory Of Knots written by Toshitake Kohno and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.

Handbook Of Knot Theory

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Author : William Menasco
language : en
Publisher: Elsevier
Release Date : 2005-08-02

Handbook Of Knot Theory written by William Menasco and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-02 with Mathematics categories.

This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry. * Survey of mathematical knot theory * Articles by leading world authorities * Clear exposition, not over-technical * Accessible to readers with undergraduate background in mathematics

Knots And Physics

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Author : Louis H. Kauffman
language : en
Publisher: World Scientific
Release Date : 1991

Knots And Physics written by Louis H. Kauffman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.

This book is an introductory explication on the theme of knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of the knot theory, coupled with a quantum statistical frame work create a context that naturally and powerfully includes an extraordinary range of interelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward the knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related with and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics, knots in dynamical systems.

The Knot Book

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Author : Colin Conrad Adams
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

The Knot Book written by Colin Conrad Adams and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.

New Developments In The Theory Of Knots

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