Verfügbarkeit: Quantum Invariants of Knots and 3-Manifolds

Quantum Invariants of Knots and 3-Manifolds:

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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1. Verfasser:	Turaev, Vladimir G. (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Berlin ; Boston De Gruyter [2020]
Ausgabe:	Reprint 2020
Schriftenreihe:	De Gruyter Studies in Mathematics 18
Schlagworte:	MATHEMATICS / General Dimension 3 Knoten > Mathematik Mannigfaltigkeit Monoidale Kategorie Topologische Mannigfaltigkeit Topologische Invariante Topologie Knotentheorie Quantenfeldtheorie
Online-Zugang:	FAW01 FHA01 FKE01 FLA01 UPA01 FAB01 FCO01 UBM01 UBT01 UBY01 URL des Erstveröffentlichers
Zusammenfassung:	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
Beschreibung:	Description based on online resource; title from PDF title page (publisher's Web site, viewed 06. Apr 2020)
Beschreibung:	1 online resource (588 pages) Num. figs
ISBN:	9783110883275
DOI:	10.1515/9783110883275

Internformat

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id	DE-604.BV046669360
illustrated	Not Illustrated
index_date	2024-07-03T14:21:07Z
indexdate	2024-07-10T08:50:48Z
institution	BVB
isbn	9783110883275
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-032080363
oclc_num	1151410823
open_access_boolean
owner	DE-1046 DE-Aug4 DE-859 DE-860 DE-739 DE-1043 DE-858 DE-19 DE-BY-UBM DE-703 DE-706
owner_facet	DE-1046 DE-Aug4 DE-859 DE-860 DE-739 DE-1043 DE-858 DE-19 DE-BY-UBM DE-703 DE-706
physical	1 online resource (588 pages) Num. figs
psigel	ZDB-23-DGG ZDB-23-GMA ZDB-23-GBA ZDB-23-GMA_1990/1999 ZDB-23-DGG FAW_PDA_DGG ZDB-23-DGG FHA_PDA_DGG ZDB-23-DGG FKE_PDA_DGG ZDB-23-DGG FLA_PDA_DGG ZDB-23-DGG UPA_PDA_DGG ZDB-23-DGG FAB_PDA_DGG ZDB-23-DGG FCO_PDA_DGG ZDB-23-GBA ZDB-23-GBA_1990/1999 ZDB-23-GMA ZDB-23-GMA_1990/1999
publishDate	2020
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publisher	De Gruyter
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series2	De Gruyter Studies in Mathematics
spelling	Turaev, Vladimir G. Verfasser aut Quantum Invariants of Knots and 3-Manifolds Vladimir G. Turaev Reprint 2020 Berlin ; Boston De Gruyter [2020] © 1994 1 online resource (588 pages) Num. figs txt rdacontent c rdamedia cr rdacarrier De Gruyter Studies in Mathematics 18 Description based on online resource; title from PDF title page (publisher's Web site, viewed 06. Apr 2020) 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 In English MATHEMATICS / General bisacsh Dimension 3 (DE-588)4321722-9 gnd rswk-swf Knoten Mathematik (DE-588)4164314-8 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Monoidale Kategorie (DE-588)4170466-6 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Topologische Invariante (DE-588)4310559-2 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Knotentheorie (DE-588)4164318-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s Knoten Mathematik (DE-588)4164314-8 s Topologische Invariante (DE-588)4310559-2 s 1\p DE-604 Quantenfeldtheorie (DE-588)4047984-5 s Topologie (DE-588)4060425-1 s Monoidale Kategorie (DE-588)4170466-6 s 2\p DE-604 Topologische Mannigfaltigkeit (DE-588)4185712-4 s Knotentheorie (DE-588)4164318-5 s 3\p DE-604 Erscheint auch als Druck-Ausgabe 9783110137040 https://doi.org/10.1515/9783110883275 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Turaev, Vladimir G. Quantum Invariants of Knots and 3-Manifolds MATHEMATICS / General bisacsh Dimension 3 (DE-588)4321722-9 gnd Knoten Mathematik (DE-588)4164314-8 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Monoidale Kategorie (DE-588)4170466-6 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Topologische Invariante (DE-588)4310559-2 gnd Topologie (DE-588)4060425-1 gnd Knotentheorie (DE-588)4164318-5 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd
subject_GND	(DE-588)4321722-9 (DE-588)4164314-8 (DE-588)4037379-4 (DE-588)4170466-6 (DE-588)4185712-4 (DE-588)4310559-2 (DE-588)4060425-1 (DE-588)4164318-5 (DE-588)4047984-5
title	Quantum Invariants of Knots and 3-Manifolds
title_auth	Quantum Invariants of Knots and 3-Manifolds
title_exact_search	Quantum Invariants of Knots and 3-Manifolds
title_exact_search_txtP	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_short	Quantum Invariants of Knots and 3-Manifolds
title_sort	quantum invariants of knots and 3 manifolds
topic	MATHEMATICS / General bisacsh Dimension 3 (DE-588)4321722-9 gnd Knoten Mathematik (DE-588)4164314-8 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Monoidale Kategorie (DE-588)4170466-6 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Topologische Invariante (DE-588)4310559-2 gnd Topologie (DE-588)4060425-1 gnd Knotentheorie (DE-588)4164318-5 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd
topic_facet	MATHEMATICS / General Dimension 3 Knoten Mathematik Mannigfaltigkeit Monoidale Kategorie Topologische Mannigfaltigkeit Topologische Invariante Topologie Knotentheorie Quantenfeldtheorie
url	https://doi.org/10.1515/9783110883275
work_keys_str_mv	AT turaevvladimirg quantuminvariantsofknotsand3manifolds

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