Quantum Invariants of Knots and 3-Manifolds / / Vladimir G. Turaev.
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 su...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2020] ©1994 |
Year of Publication: | 2020 |
Edition: | Reprint 2020 |
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. Reprint 2020 Berlin ; Boston : De Gruyter, [2020] ©1994 1 online resource (588 p.) : Num. figs. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Studies in Mathematics , 0179-0986 ; 18 Frontmatter -- 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 -- Problems -- References -- Subject index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. 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) Quantum field theory. MATHEMATICS / General. bisacsh Title is part of eBook package: De Gruyter DGBA Mathematics - 1990 - 1999 9783110637199 ZDB-23-GMA print 9783110137040 https://doi.org/10.1515/9783110883275 https://www.degruyter.com/isbn/9783110883275 Cover https://www.degruyter.com/document/cover/isbn/9783110883275/original |
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English |
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Turaev, Vladimir G., Turaev, Vladimir G., |
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Turaev, Vladimir G., Turaev, Vladimir G., Quantum Invariants of Knots and 3-Manifolds / De Gruyter Studies in Mathematics , Frontmatter -- 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 -- Problems -- 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 -- 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 -- Problems -- 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 |
2020 |
physical |
1 online resource (588 p.) : Num. figs. Issued also in print. |
edition |
Reprint 2020 |
contents |
Frontmatter -- 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 -- Problems -- References -- Subject index |
isbn |
9783110883275 9783110637199 9783110137040 |
issn |
0179-0986 ; |
url |
https://doi.org/10.1515/9783110883275 https://www.degruyter.com/isbn/9783110883275 https://www.degruyter.com/document/cover/isbn/9783110883275/original |
illustrated |
Not Illustrated |
doi_str_mv |
10.1515/9783110883275 |
oclc_num |
1149402321 |
work_keys_str_mv |
AT turaevvladimirg quantuminvariantsofknotsand3manifolds |
status_str |
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ids_txt_mv |
(DE-B1597)55547 (OCoLC)1149402321 |
carrierType_str_mv |
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hierarchy_parent_title |
Title is part of eBook package: De Gruyter DGBA Mathematics - 1990 - 1999 |
is_hierarchy_title |
Quantum Invariants of Knots and 3-Manifolds / |
container_title |
Title is part of eBook package: De Gruyter DGBA Mathematics - 1990 - 1999 |
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1806144763560198144 |
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