Quantum Invariants of Knots and 3-Manifolds / / Vladimir G. Turaev.
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...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2016] ©2016 |
Year of Publication: | 2016 |
Edition: | 3rd corr. ed. |
Language: | English |
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Turaev, Vladimir G., author. aut http://id.loc.gov/vocabulary/relators/aut Quantum Invariants of Knots and 3-Manifolds / Vladimir G. Turaev. 3rd corr. ed. Berlin ; Boston : De Gruyter, [2016] ©2016 1 online resource (596 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Studies in Mathematics , 0179-0986 ; 18 Frontmatter -- Preface -- Contents -- Introduction -- Part I. Towards Topological Field Theory -- Chapter I. Invariants of graphs in Euclidean 3-space -- Chapter II. Invariants of closed 3-manifolds -- Chapter III. Foundations of topological quantum field theory -- Chapter IV. Three-dimensional topological quantum field theory -- Chapter V. Two-dimensional modular functors -- Part II. The Shadow World -- Chapter VI. 6j-symbols -- Chapter VII. Simplicial state sums on 3-manifolds -- Chapter VIII. Generalities on shadows -- Chapter IX. Shadows of manifolds -- Chapter X. State sums on shadows -- Part III. Towards Modular Categories -- Chapter XI. An algebraic construction of modular categories -- Chapter XII. A geometric construction of modular categories -- Appendix I. Dimension and trace re-examined -- Appendix II. Vertex models on link diagrams -- Appendix III. Gluing re-examined -- Appendix IV. The signature of closed 4-manifolds from a state sum -- References -- Subject index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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 Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Knotentheorie. Mannigfaltigkeit. Topologie. Topologische Algebra. Topologische Gruppe. MATHEMATICS / Algebra / General. bisacsh Title is part of eBook package: De Gruyter DG Plus DeG Package 2016 Part 1 9783110762501 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2016 9783110701005 Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package 9783110494938 ZDB-23-GSM Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2016 9783110485103 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2016 9783110485288 ZDB-23-DMA EPUB 9783110434569 print 9783110442663 https://doi.org/10.1515/9783110435221 https://www.degruyter.com/isbn/9783110435221 Cover https://www.degruyter.com/document/cover/isbn/9783110435221/original |
language |
English |
format |
eBook |
author |
Turaev, Vladimir G., Turaev, Vladimir G., |
spellingShingle |
Turaev, Vladimir G., Turaev, Vladimir G., Quantum Invariants of Knots and 3-Manifolds / De Gruyter Studies in Mathematics , Frontmatter -- Preface -- Contents -- Introduction -- Part I. Towards Topological Field Theory -- Chapter I. Invariants of graphs in Euclidean 3-space -- Chapter II. Invariants of closed 3-manifolds -- Chapter III. Foundations of topological quantum field theory -- Chapter IV. Three-dimensional topological quantum field theory -- Chapter V. Two-dimensional modular functors -- Part II. The Shadow World -- Chapter VI. 6j-symbols -- Chapter VII. Simplicial state sums on 3-manifolds -- Chapter VIII. Generalities on shadows -- Chapter IX. Shadows of manifolds -- Chapter X. State sums on shadows -- Part III. Towards Modular Categories -- Chapter XI. An algebraic construction of modular categories -- Chapter XII. A geometric construction of modular categories -- Appendix I. Dimension and trace re-examined -- Appendix II. Vertex models on link diagrams -- Appendix III. Gluing re-examined -- Appendix IV. The signature of closed 4-manifolds from a state sum -- References -- Subject index |
author_facet |
Turaev, Vladimir G., Turaev, Vladimir G., |
author_variant |
v g t vg vgt v g t vg vgt |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Turaev, Vladimir G., |
title |
Quantum Invariants of Knots and 3-Manifolds / |
title_full |
Quantum Invariants of Knots and 3-Manifolds / Vladimir G. Turaev. |
title_fullStr |
Quantum Invariants of Knots and 3-Manifolds / Vladimir G. Turaev. |
title_full_unstemmed |
Quantum Invariants of Knots and 3-Manifolds / Vladimir G. Turaev. |
title_auth |
Quantum Invariants of Knots and 3-Manifolds / |
title_alt |
Frontmatter -- Preface -- Contents -- Introduction -- Part I. Towards Topological Field Theory -- Chapter I. Invariants of graphs in Euclidean 3-space -- Chapter II. Invariants of closed 3-manifolds -- Chapter III. Foundations of topological quantum field theory -- Chapter IV. Three-dimensional topological quantum field theory -- Chapter V. Two-dimensional modular functors -- Part II. The Shadow World -- Chapter VI. 6j-symbols -- Chapter VII. Simplicial state sums on 3-manifolds -- Chapter VIII. Generalities on shadows -- Chapter IX. Shadows of manifolds -- Chapter X. State sums on shadows -- Part III. Towards Modular Categories -- Chapter XI. An algebraic construction of modular categories -- Chapter XII. A geometric construction of modular categories -- Appendix I. Dimension and trace re-examined -- Appendix II. Vertex models on link diagrams -- Appendix III. Gluing re-examined -- Appendix IV. The signature of closed 4-manifolds from a state sum -- References -- Subject index |
title_new |
Quantum Invariants of Knots and 3-Manifolds / |
title_sort |
quantum invariants of knots and 3-manifolds / |
series |
De Gruyter Studies in Mathematics , |
series2 |
De Gruyter Studies in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2016 |
physical |
1 online resource (596 p.) Issued also in print. |
edition |
3rd corr. ed. |
contents |
Frontmatter -- Preface -- Contents -- Introduction -- Part I. Towards Topological Field Theory -- Chapter I. Invariants of graphs in Euclidean 3-space -- Chapter II. Invariants of closed 3-manifolds -- Chapter III. Foundations of topological quantum field theory -- Chapter IV. Three-dimensional topological quantum field theory -- Chapter V. Two-dimensional modular functors -- Part II. The Shadow World -- Chapter VI. 6j-symbols -- Chapter VII. Simplicial state sums on 3-manifolds -- Chapter VIII. Generalities on shadows -- Chapter IX. Shadows of manifolds -- Chapter X. State sums on shadows -- Part III. Towards Modular Categories -- Chapter XI. An algebraic construction of modular categories -- Chapter XII. A geometric construction of modular categories -- Appendix I. Dimension and trace re-examined -- Appendix II. Vertex models on link diagrams -- Appendix III. Gluing re-examined -- Appendix IV. The signature of closed 4-manifolds from a state sum -- References -- Subject index |
isbn |
9783110435221 9783110762501 9783110701005 9783110494938 9783110485103 9783110485288 9783110434569 9783110442663 |
issn |
0179-0986 ; |
url |
https://doi.org/10.1515/9783110435221 https://www.degruyter.com/isbn/9783110435221 https://www.degruyter.com/document/cover/isbn/9783110435221/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
514 - Topology |
dewey-full |
514.2 |
dewey-sort |
3514.2 |
dewey-raw |
514.2 |
dewey-search |
514.2 |
doi_str_mv |
10.1515/9783110435221 |
oclc_num |
958054778 |
work_keys_str_mv |
AT turaevvladimirg quantuminvariantsofknotsand3manifolds |
status_str |
n |
ids_txt_mv |
(DE-B1597)456467 (OCoLC)958054778 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2016 Part 1 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2016 Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2016 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2016 |
is_hierarchy_title |
Quantum Invariants of Knots and 3-Manifolds / |
container_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2016 Part 1 |
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fullrecord |
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