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Quantum Invariants of Knots and 3-Manifolds, Vladimir G. Turaev


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Автор: Vladimir G. Turaev
Название:  Quantum Invariants of Knots and 3-Manifolds
ISBN: 9783110442663
Издательство: Walter de Gruyter
Классификация:



ISBN-10: 3110442663
Обложка/Формат: Hardback
Страницы: 608
Вес: 1.13 кг.
Дата издания: 11.07.2016
Серия: Mathematics
Язык: English
Размер: 244 x 175 x 36
Читательская аудитория: Professional and scholarly
Ключевые слова: Algebra,Geometry,Quantum physics (quantum mechanics & quantum field theory), MATHEMATICS / Algebra / General,MATHEMATICS / Geometry / General,SCIENCE / Physics / Quantum Theory
Основная тема: MATHEMATICS / Algebra / General,MATHEMATICS / Geometry / General
Ссылка на Издательство: Link
Поставляется из: Германии
Описание: 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


Euclidean Quantum Gravity on Manifolds with Boundary

Автор: Giampiero Esposito; A.Yu. Kamenshchik; G. Pollifro
Название: Euclidean Quantum Gravity on Manifolds with Boundary
ISBN: 9401064520 ISBN-13(EAN): 9789401064521
Издательство: Springer
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Цена: 14365.00 р.
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Описание: The following chapters are devoted to the standard theory of the effective action and the geometric im- provement due to Vilkovisky, the manifestly covariant quantization of gauge fields, zeta-function regularization in mathematics and in quantum field theory, and the problem of boundary conditions in one-loop quantum theory.

Algebraic Invariants Of Links (2Nd Edition)

Автор: Hillman Jonathan
Название: Algebraic Invariants Of Links (2Nd Edition)
ISBN: 9814407380 ISBN-13(EAN): 9789814407380
Издательство: World Scientific Publishing
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Цена: 19008.00 р.
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Описание: Serves as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. This second edition introduces two new chapters - twisted polynomial invariants and singularities of plane curves. Each replaces brief sketches in the first edition.

Автор: Clifford Henry Taubes
Название: Seiberg Witten and Gromov Invariants for Symplectic 4-manifolds
ISBN: 1571460616 ISBN-13(EAN): 9781571460615
Издательство: Oxford Academ
Цена: 5378.00 р.
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Описание: This work offers the proof of the remarkable relationship between Seiberg-Witten and Gromov invariants on symplectic 4-manifolds. It is a companion to "Topics on Symplectic 4-Manifolds" published in 1998 and brings together articles published in two American journals.

Lecture Notes on Knot Invariants

Автор: Li Weiping
Название: Lecture Notes on Knot Invariants
ISBN: 9814675962 ISBN-13(EAN): 9789814675963
Издательство: World Scientific Publishing
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Цена: 5069.00 р.
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Описание:

The volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry. It presents the detailed Hecke algebra and braid representation to illustrate the original Jones polynomial (rather than the algebraic formal definition many other books and research articles use) and provides self-contained proofs of the Tait conjecture (one of the big achievements from the Jones invariant). It also presents explicit computations to the Casson-Lin invariant via braid representations.

With the approach of an explicit computational point of view on knot invariants, this user-friendly volume will benefit readers to easily understand low-dimensional topology from examples and computations, rather than only knowing terminologies and theorems.

Invariants of Quadratic Differential Forms

Автор: Wright
Название: Invariants of Quadratic Differential Forms
ISBN: 1107493935 ISBN-13(EAN): 9781107493933
Издательство: Cambridge Academ
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Цена: 3008.00 р.
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Описание: Originally published in 1908 in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding the invariant theory connected with a single quadratic differential form. This book will be of value to anyone with an interest in quadratic differential forms and the history of mathematics.

Moments and Moment Invariants in Pattern Recognition

Автор: Flusser, Jan.
Название: Moments and Moment Invariants in Pattern Recognition
ISBN: 0470699876 ISBN-13(EAN): 9780470699874
Издательство: Wiley
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Цена: 15515.00 р.
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Описание: Moments and Moment Invariants in Pattern Recognition presents a survey of fundamental and topical pattern recognition methods based on image moments. The authors expound on the establishment of the use of invariant moments in pattern recognition and continue by presenting a systematic review of the basic definitions and properties of moments.

Topological Invariants of Stratified Spaces

Автор: Markus Banagl
Название: Topological Invariants of Stratified Spaces
ISBN: 3642072488 ISBN-13(EAN): 9783642072482
Издательство: Springer
Цена: 13974.00 р.
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Описание: The homology of manifolds enjoys a remarkable symmetry: Poincare duality. If the manifold is triangulated, then this duality can be established by associating to a s- plex its dual block in the barycentric subdivision. In a manifold, the dual block is a cell, so the chain complex based on the dual blocks computes the homology of the manifold. Poincare duality then serves as a cornerstone of manifold classi cation theory. One reason is that it enables the de nition of a fundamental bordism inva- ant, the signature. Classifying manifolds via the surgery program relies on modifying a manifold by executing geometric surgeries. The trace of the surgery is a bordism between the original manifold and the result of surgery. Since the signature is a b- dism invariant, it does not change under surgery and is thus a basic obstruction to performing surgery. Inspired by Hirzebruch's signature theorem, a method of Thom constructs characteristic homology classes using the bordism invariance of the s- nature. These classes are not in general homotopy invariants and consequently are ne enough to distinguish manifolds within the same homotopy type. Singular spaces do not enjoy Poincare duality in ordinary homology. After all, the dual blocks are not cells anymore, but cones on spaces that may not be spheres. This book discusses when, and how, the invariants for manifolds described above can be established for singular spaces.


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