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Subfactors And Knots

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Subfactors And Knots

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Author : Vaughan F. R. Jones
language : en
Publisher: American Mathematical Soc.
Release Date : 1991

Subfactors And Knots written by Vaughan F. R. Jones 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 1991 with Mathematics categories.

This book is based on a set of lectures presented by the author at the NSF-CBMS Regional Conference, Applications of Operator Algebras to Knot Theory and Mathematical Physics, held at the U.S. Naval Academy in Annapolis in June 1988. The audience consisted of low-dimensional topologists and operator algebraists, so the speaker attempted to make the material comprehensible to both groups. He provides an extensive introduction to the theory of von Neumann algebras and to knot theory and braid groups. The presentation follows the historical development of the theory of subfactors and the ensuing applications to knot theory, including full proofs of some of the major results. The author treats in detail the Homfly and Kauffman polynomials, introduces statistical mechanical methods on knot diagrams, and attempts an analogy with conformal field theory. Written by one of the foremost mathematicians of the day, this book will give readers an appreciation of the unexpected interconnections between different parts of mathematics and physics.

Subfactors And Knots

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Author : Vaughan F. R. Jones
language : en
Publisher: American Mathematical Soc.
Release Date :

This book is based on a set of lectures presented by the author at the NSF-CBMS Regional Conference, Applications of Operator Algebras to Knot Theory and Mathematical Physics, held at the US Naval Academy in Annapolis in June 1988. The audience consisted of low-dimensional topologists and operator algebraists, so the speaker attempted to make the material comprehensible to both groups. He provides an extensive introduction to the theory of von Neumann algebras and to knot theory and braid groups. The presentation follows the historical development of the theory of subfactors and the ensuing applications to knot theory, including full proofs of some of the major results. The author treats in detail the Homfly and Kauffman polynomials, introduces statistical mechanical methods on knot diagrams, and attempts an analogy with conformal field theory. Written by one of the foremost mathematicians of the day, this book will give readers an appreciation of the unexpected interconnections between different parts of mathematics and physics.

Quantum Invariants Of Knots And 3 Manifolds

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Author : Vladimir G. Turaev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-07-11

Quantum Invariants Of Knots And 3 Manifolds written by Vladimir G. Turaev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-11 with Mathematics categories.

Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups.The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space.This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents:Invariants of graphs in Euclidean 3-space and of closed 3-manifoldsFoundations of topological quantum field theoryThree-dimensional topological quantum field theoryTwo-dimensional modular functors6j-symbolsSimplicial state sums on 3-manifoldsShadows of manifolds and state sums on shadowsConstructions of modular categories

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

Lectures In Knot Theory

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Author : Józef H. Przytycki
language : en
Publisher: Springer Nature
Release Date :

Lectures In Knot Theory written by Józef H. Przytycki and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Braid Group Knot Theory And Statistical Mechanics

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Author : Mo-lin Ge
language : en
Publisher: World Scientific
Release Date : 1991-06-05

Braid Group Knot Theory And Statistical Mechanics written by Mo-lin Ge and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-06-05 with Science categories.

Contents:Notes on Subfactors and Statistical Mechanics (V F R Jones)Polynomial Invariants in Knot Theory (L H Kauffman)Algebras of Loops on Surfaces, Algebras of Knots, and Quantization (V G Turaev)Quantum Groups (L Faddeev et al.)Introduction to the Yang-Baxter Equation (M Jimbo)Integrable Systems Related to Braid Groups and Yang-Baxter Equation (T Kohno)The Yang-Baxter Relation: A New Tool for Knot Theory (Y Akutsu et al.)Akutsu-Wadati Link Polynomials from Feynman-Kauffman Diagrams (M-L Ge et al.)Quantum Field Theory and the Jones Polynomial (E Witten) Readership: Mathematical physicists.

Gauge Fields Knots And Gravity

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Author : John Baez
language : en
Publisher: World Scientific Publishing Company
Release Date : 1994-10-24

Gauge Fields Knots And Gravity written by John Baez and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-24 with Science categories.

This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.

History And Science Of Knots

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Author : John Christopher Turner
language : en
Publisher: World Scientific
Release Date : 1996

History And Science Of Knots written by John Christopher Turner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Crafts & Hobbies categories.

In view of the explosion of mathematical theories of knots in the past decade, with consequential applications, this book sets down a brief, fragmentary history of mankind's oldest and most useful technical and decorative device - the knot.

A Survey Of Knot Theory

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Author : Akio Kawauchi
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

A Survey Of Knot Theory written by Akio Kawauchi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.

Subfactors And Knots

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