Introduction To Vassiliev Knot Invariants

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Introduction To Vassiliev Knot Invariants

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Author : S. Chmutov
language : en
Publisher: Cambridge University Press
Release Date : 2012-05-24

Introduction To Vassiliev Knot Invariants written by S. Chmutov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.

A detailed exposition of the theory with an emphasis on its combinatorial aspects.

An Introduction To Quantum And Vassiliev Knot Invariants

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Author : David M. Jackson
language : en
Publisher: Springer
Release Date : 2019-05-04

An Introduction To Quantum And Vassiliev Knot Invariants written by David M. Jackson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-04 with Mathematics categories.

This book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant. Consisting of four parts, the book opens with an introduction to the fundamentals of knot theory, and to knot invariants such as the Jones polynomial. The second part introduces quantum invariants of knots, working constructively from first principles towards the construction of Reshetikhin-Turaev invariants and a description of how these arise through Drinfeld and Jimbo's quantum groups. Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. This is a universal quantum invariant and a universal Vassiliev invariant, and brings together these two seemingly different families of knot invariants. The book provides a detailed account of the construction of the Jones polynomial via the quantum groups attached to sl(2), the Vassiliev weight system arising from sl(2), and how these invariants come together through the Kontsevich invariant.

Introduction To Vassiliev Knot Invariants

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Author : Sergei Chmutov
language : en
Publisher:
Release Date : 2014-05-14

Introduction To Vassiliev Knot Invariants written by Sergei Chmutov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.

With hundreds of worked examples, exercises and illustrations, this detailed exposition of the theory of Vassiliev knot invariants opens the field to students with little or no knowledge in this area. It also serves as a guide to more advanced material. The book begins with a basic and informal introduction to knot theory, giving many examples of knot invariants before the class of Vassiliev invariants is introduced. This is followed by a detailed study of the algebras of Jacobi diagrams and 3-graphs, and the construction of functions on these algebras via Lie algebras. The authors then describe two constructions of a universal invariant with values in the algebra of Jacobi diagrams: via iterated integrals and via the Drinfeld associator, and extend the theory to framed knots. Various other topics are then discussed, such as Gauss diagram formulae, before the book ends with Vassiliev's original construction.

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.

Knots Links Braids And 3 Manifolds

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Author : V. V. Prasolov
language : en
Publisher: American Mathematical Soc.
Release Date :

Knots Links Braids And 3 Manifolds written by V. V. Prasolov 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 with Science categories.

This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. The mathematical prerequisites are minimal compared to other monographs in this area. Numerous figures and problems make this book suitable as a graduate level course text or for self-study.

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 knot theory from its very beginnings to today's most recent research results. The topics include Alexander polynomials, Jones type polynomials, and Vassiliev invariants. With its appendix containing many useful tables and an extended list of references with over 3,500 entries it is an indispensable book for everyone concerned with knot theory. The book can serve as an introduction to the field for advanced undergraduate and graduate students. Also researchers working in outside areas such as theoretical physics or molecular biology will benefit from this thorough study which is complemented by many exercises and examples.

Quantum Invariants

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Author : Tomotada Ohtsuki
language : en
Publisher: World Scientific
Release Date : 2002

Quantum Invariants written by Tomotada Ohtsuki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.

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 Chern-Simons field theory and the Wess-Zumino-Witten model are described as the physical background of the invariants.

Knots

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Author : Alekseĭ Bronislavovich Sosinskiĭ
language : en
Publisher: Harvard University Press
Release Date : 2002

Knots written by Alekseĭ Bronislavovich Sosinskiĭ and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

This book, written by a mathematician known for his own work on knot theory, is a clear, concise, and engaging introduction to this complicated subject, and a guide to the basic ideas and applications of knot theory. 63 illustrations.

Graphs On Surfaces And Their Applications

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Author : Sergei K. Lando
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-12-01

Graphs On Surfaces And Their Applications written by Sergei K. Lando 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 2003-12-01 with Mathematics categories.

Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.

Knots And Links

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Author : Peter R. Cromwell
language : en
Publisher: Cambridge University Press
Release Date : 2004-10-14

Knots And Links written by Peter R. Cromwell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-14 with Mathematics categories.

A richly illustrated 2004 textbook on knot theory; minimal prerequisites but modern in style and content.