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Quantum Invariants Of Knots And 3 Manifolds

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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 Invariants categories.

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 : 2020-03-23

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 2020-03-23 with Mathematics categories.

This monograph provides a systematic treatment of topological quantum field theories (TQFT's) in three dimensions, inspired by the discovery of the Jones polynomial of knots, the Witten-Chern-Simons field theory, and the theory of quantum groups. The author, one of the leading experts in the subject, gives a rigorous and self-contained exposition of new fundamental algebraic and topological concepts that emerged in this theory. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFT's and 2-dimensional modular functors from so-called modular categories. This gives new knot and 3-manifold invariants as well as linear representations of the mapping class groups of surfaces. In Part II the machinery of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFT's constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and Kauffman's skein modules. This book is accessible to graduate students in mathematics and physics with a knowledge of basic algebra and topology. It will be an indispensable source for everyone who wishes to enter the forefront of this rapidly growing and fascinating area at the borderline of mathematics and physics. Most of the results and techniques presented here appear in book form for the first time.

Quantum Invariants Of Knots And 3 Manifolds

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Author : Vladimir Turaev
language : en
Publisher:
Release Date : 1994

Quantum Invariants Of Knots And 3 Manifolds written by Vladimir Turaev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.

Invariants Of Knots And 3 Manifolds Kyoto 2001

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

Invariants Of Knots And 3 Manifolds Kyoto 2001 written by Tomotada Ohtsuki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Knot theory categories.

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

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

Quantum Groups And Knot Invariants

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Author : Christian Kassel
language : en
Publisher:
Release Date : 1997

Quantum Groups And Knot Invariants written by Christian Kassel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Categories (Mathematics) categories.

This book provides a concise introduction to quantum groups, braided monoidal categories and quantum invariants of knots and of three-dimensional manifolds. The exposition emphasizes the newly discovered deep relationships between these areas.

Quantum Topology

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Author : Louis H. Kauffman
language : en
Publisher: World Scientific
Release Date : 1993

Quantum Topology 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 1993 with Mathematics categories.

This book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants were rapidly connected with quantum groups and methods in statistical mechanics. This was followed by Edward Witten's introduction of methods of quantum field theory into the subject and the formulation by Witten and Michael Atiyah of the concept of topological quantum field theories.This book is a review volume of on-going research activity. The papers derive from talks given at the Special Session on Knot and Topological Quantum Field Theory of the American Mathematical Society held at Dayton, Ohio in the fall of 1992. The book consists of a self-contained article by Kauffman, entitled Introduction to Quantum Topology and eighteen research articles by participants in the special session.This book should provide a useful source of ideas and results for anyone interested in the interface between topology and quantum field theory.

Knots Links Braids And 3 Manifolds

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Author : Viktor Vasilʹevich Prasolov
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Knots Links Braids And 3 Manifolds written by Viktor Vasilʹevich 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 1997 with Mathematics 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.

Some Background To V G Turaev S Quantum Invariants Of 3 Manifolds

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Author : Pieter Cornelis Griend
language : en
Publisher:
Release Date : 1993

Some Background To V G Turaev S Quantum Invariants Of 3 Manifolds written by Pieter Cornelis Griend and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Invariants categories.

Quantum Invariants

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Author : Tomotada Ohtsuki
language : en
Publisher: World Scientific
Release Date : 2001-12-21

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. Contents: Knots and Polynomial InvariantsBraids and Representations of the Braid GroupsOperator Invariants of Tangles via Sliced DiagramsRibbon Hopf Algebras and Invariants of LinksMonodromy Representations of the Braid Groups Derived from the Knizhnik–Zamolodchikov EquationThe Kontsevich InvariantVassiliev InvariantsQuantum Invariants of 3-ManifoldsPerturbative Invariants of Knots and 3-ManifoldsThe LMO InvariantFinite Type Invariants of Integral Homology 3-Spheres Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics. Keywords:Kontsevich Invariant;LMO Invariant;Quantum Groups;Knot;3-Manifold;Quantum Invariant;Vassiliev Invariant;Finite Type Invariant;Chord Diagram;Jacobi Diagram;KZ Equation;Chern-Simons TheoryReviews:“This is a nicely written and useful book: I think that the author has done a great job in explaining quantum invariants of knots and 3-manifolds also on an intuitive and well-motivated, organically growing and not too technical level, at the same time however presenting a lot of material ordered by a clear guiding line.”Mathematics Abstracts “Ohtsuki's book is a very valuable addition to the literature. It surveys the full spectrum of work in the area of quantum invariants … Ohtsuk's book is very readable, for he makes an attempt to present the material in as straightforward a way as possible … the presentation here is very clear and should be easily accessible … this is an excellent book which I would recommend to beginners wanting to learn about quantum invariants and to experts alike.”Mathematical Reviews

Quantum Invariants Of Knots And 3 Manifolds

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