Verfügbarkeit: Quantum invariants of knots and 3-manifolds

Quantum invariants of knots and 3-manifolds:

Gespeichert in:

Bibliographische Detailangaben
1. Verfasser:	Turaev, Vladimir G. 1954- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin/Boston De Gruyter [2016]
Ausgabe:	3rd edition
Schriftenreihe:	De Gruyter Studies in Mathematics 18
Schlagworte:	Knotentheorie Topologische Mannigfaltigkeit Topologie Mannigfaltigkeit Knoten > Mathematik Monoidale Kategorie Topologische Invariante Dimension 3 Quantenfeldtheorie
Online-Zugang:	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110442663&searchTitles=true Inhaltsverzeichnis
Beschreibung:	xii, 596 Seiten Illustrationen, Diagramme 24 cm x 17 cm
ISBN:	9783110435238 9783110442663

Internformat

MARC


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Datensatz im Suchindex

_version_	1804176471313350656
adam_text	CONTENTS INTRODUCTION................................................................................................................. 1 P A RT I. TOWARDS TOPOLOGICAL FIELD T H E O R Y ..................................................... 15 CHAPTER 1 INVARIANTS OF 17 1 RIBBON CATEGORIES............................................................................................. 17 2. OPERATOR INVIIANTS OF RIBBON GRAPHS.............................................................. 30 3 REDUCTION OF THEOREM 2.5 TO 1 ^ * ..............................................................49 4. PROOF OF LEM MAS............................................................................................... 57 N OTES......................................................................................................................... 71 CHAPTER II. INVARIANTS OF CLOSED * -MANIFOLDS........................................................ 72 1. MODULAR IENSOR CATEGORIES............................................................................... 72 2 I N V A R I* S OF 3M IR 0 1 D S ................................................................................ 78 3. PROOF OF L O R E M 2.3.2. ACTION OF 5 (2, Z ) ............................................... 84 4. COMPUTATIONS IN SEMISIMPLE CATEGORIES.......................................................... 99 5 HERMITIAN AND UNITARY CATEGORIES................................................................. 108 NOTES......................................................... 116 CHAPTER III. FOUNDATIONS OF TOPOLOGICAL QUANTUM FIELD THEORY ...... 118 1 AXIOMATIC DEFINITION OF TQFTS ................................................................. 118 2. FUNDAMENTAL PROPERTIES................................................................................. 127 3 ISOM OIPHISM SOFTQ FTS .............................................................................. 132 4. QUANTUM INVARIANTS......................................................................................... 136 5 HERMITIAN AND UNITARY TQFTS ................................................................... 142 6 ELIMINATION OF ANOMALIES.............................................................................. 145 N OTES....................................................................................................................... 150 CHAPTER IV. THREE-DIMENSIONAL TOPOLOGICAL QUANTUM FIELD THEORY. ........ 152 1 THREE-DIMENSIONAL TQFT: PRELIMINARY VERSION.......................................... 152 2 PROOF OF L O R E M 1.9..................................................................................... 162 J. LAGRANGIAN RELATIONS AND MASLOV IN D IC E S .................................................. 179 4. COMPUTATION OF ANOM ALIES............................................................................ 186 DEFINITION OF SHADOWS .................................... MISCELLANEOUS DEFINITIONS AND CONSTRICTIONS SHADOW L IN K S ................................................. CHAPTER VIII. GENERALITIES ON SHADOWS 367 367 371 376 5 ACTION OF THE MODULAR G RO U P O ID ................................................................. 190 6 RENORMALIZED -DIMENSIONAL TQFT.............................................................. 196 7. COMPUTATIONS IN THE RENORMALIZED T Q F T .................................................. 207 8 ABSOLUTE ANOMALY-FREE T Q F T ...................................................................... 210 9. ANOMALY-FREE TQFT...................................................................................... 213 10 HERMITIEN TQFT ............................................................................................ 217 11. UNITARY TQFT................................................................................................. 223 12 VERIINDE ALGEBRA ............................................................................................ 226 N OTES....................................................................................................................... 234 CHAPTER V. TWO-DIMENSIONAL MODULAR FU N CTO RS............................................... 236 1. AXIOMS FOR A 2DIMENSIONAL MODULAR FUNCTOR............................................. 236 2. UNDERLYING RIBBON CATEGORY........................................................................... 247 3 WEAK AND MIRROR MODULAR FUNCTORS............................................................. 266 4 CONSTRUCTION OF MODULAR FU N CTO RS............................................................... 268 5. CONSTRUCTION OF MODULAR FUNCTORS CONTINUED.............................................. 274 N OTES....................................................................................................................... 297 P A RT II. THE SHADOW W O R L D ............................................................................. 299 CHAPTER VI. 6 -SYM BOLS ....................................................................................... 301 1. ALGEBRAIC APPROACH TO 301 2. UNIMODAL CATEGORIES....................................................................................... 310 3 SYMMETRIZED MULTIPLICITY M O D U LE S............................................................. 312 4 FRAMED G RA P H S ............................................................................................... 318 5. GEOMETRIC APPROACH TO 67 * * * ............................................................. 331 N OTES....................................................................................................................... 344 CHAPTER VII SIMPLICIAL STATE SUMS ON -M ANIFOLDS .......................................... 345 1. STATE SUM MODELS ON TRIANGULATED 3 MANIF 01 D S ............................................ 345 2. PROOF OF L O R E M S 1.4 * 1.7 ....... * .* ....................... 351 3 SIMPLICIAL D IM E N SIO N A L T Q F T ................................................................. 356 4 COMPARISON OF TWO APPROACHES................................................................... 361 1 2 3 4 SURGERIES ** SHADOWS.................................................................................... 382 5 BILINEAR FORMS OF SHADOWS........................................................................... 386 6 INTEGER SHADOW S............................................................ 388 7 SHADOW GRAPHS............................................................................................... 391 N OTES....................................................................................................................... 393 CHAPTER IX. SHADOWS OF M ANIFOLDS..................................................................... 394 1 SHADOWS OF 4_MA!UEFOLDS................................................................................ 394 2 SHADOWS OF 3_MA!!IFOLDS................................................................................ 400 3 S H A D _ OF LINKS IN -MANIFOLDS................................................................. 405 4. SHADOWS OF 4-MANIFOLDS VIA HANDLE DECOMPOSITIONS ...... 410 5 COMPARISON OF BILINEAR FO RM S ..................................................................... 413 6 THICKENING OF SHADOWS.................................................................................. 417 7 PROOF OF I O R E M S 1.5 AND 1.7-1.11........................................................... 427 8 SHADOWS OF FRAMED GRAPHS............................................................................ 431 NNTPG 434 CHAPTER X. STATE SUMS ON SHADOWS...................................................................... 435 1. STATE SUM MODELS ON SHADOWED POLYHEDRA................................................ 435 2 STATE SUM INVARIANTS OF SHADOW S................................................................. 444 3. INVARIANTS OF -MANIFOLDS FROM THE SHADOW VIEWPOINT. .............. 450 4. REDUCTION OF THEOREM 3.3 TO A LEM M A........................................................ 452 5 PASSAGE TO THE SHADOW WORLD ....................................................................... 455 6 PROOF OF THEOREM 5.6.................................................................................... 463 7. INV^IANTS OF FRAMED GRAPHS FROM THE SHADOW VIEWPOINT. ............ 473 8 PROOF OF THEOREM V II.4 .2 ............................................................................ 477 9. COMPUTATIONS FOR GRAPH M ANIFOLDS............................................................. 484 N OTES....................................................................................................................... 489 PART III. TOWARDS MODULAR C ATEGORIES.......................................................... 491 CHAPTER XI. AN ALGEBRAIC C 0 N _ ^ 493 1. HOPS ALGEBRAS A D CATEGORIES OF ......................................... 493 2 Q UASITRI^GULAR HOPS A LG E B R A ...................................................................... 496 3 RIBBON HOPS ALGEBRAS ..................................................................................... 5 * 4. DIGRESSION ON QUASIM ODULA ^ ........................................................ 503 5 MODULAR HOPS ALGEBRAS................................................................................... 506 6. QUANTUM GROUPS AT ROOTS OF U N ITY ................................................................ 508 7. QUANTUM GROUPS WITH GENERIC PARAMETER ..................................................... 513 N OTES....................................................................................................................... 517 XII CONTENTS CHAPTER XII. A GEOMETRIC CONSTRUCTION OF MODULAR CATEGORIES ..... 518 1. SKEIN MODULES AND THE JONES 518 2 SKEIN C A TE G O RY ............................................................................................... 523 3 THE TEMPERLEYLIEB A LG E B RA ....................................................................... 526 4 THE JONESWENZL IDEM POTENTS..................................................................... 529 5. THE MATRIX 5 ................................................................................................... 535 6 REFINED SKEIN CATEGORY.................................................................................. 539 7. MODULAR AND SEMISIMPLE SKEIN CATEGORIES.................................................... 546 8 MULTIPLICITY M O D U LE S.................................................................................... 551 9. HERMITIAN AND UNITARY SKEIN CATEGORIES ...................................................... 557 N OTES....................................................................................................................... 559 APPENDIX I. DIMENSION AND TRACE RE-EXAMINED................................................. 561 APPENDIX II. VERTEX MODELS ON LINK D IAGRAM S................................................. 563 APPENDIX III. GLUING RE-EXAMINED ...................................................................... 565 APPENDIX IV. THE SIGNATURE OF CLOSED 4-MANIF01DS FROM A STATE SUM...... 568 REFERENCES............................................................................................................... 571 SUBJECT IN D E X ........................................................................................................ 593
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discipline	Physik Mathematik
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publisher	De Gruyter
record_format	marc
series	De Gruyter Studies in Mathematics
series2	De Gruyter Studies in Mathematics
spelling	Turaev, Vladimir G. 1954- (DE-588)122717791 aut Quantum invariants of knots and 3-manifolds Vladimir G. Turaev 3rd edition Berlin/Boston De Gruyter [2016] © 2016 xii, 596 Seiten Illustrationen, Diagramme 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematics 18 Knotentheorie (DE-588)4164318-5 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Knoten Mathematik (DE-588)4164314-8 gnd rswk-swf Monoidale Kategorie (DE-588)4170466-6 gnd rswk-swf Topologische Invariante (DE-588)4310559-2 gnd rswk-swf Dimension 3 (DE-588)4321722-9 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s Topologie (DE-588)4060425-1 s Monoidale Kategorie (DE-588)4170466-6 s DE-604 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 Topologische Mannigfaltigkeit (DE-588)4185712-4 s Knotentheorie (DE-588)4164318-5 s 1\p DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, EPUB 978-3-11-043456-9 Erscheint auch als Online-Ausgabe, PDF 978-3-11-043522-1 De Gruyter Studies in Mathematics 18 (DE-604)BV000005407 18 http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110442663&searchTitles=true Verlag DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029107156&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Turaev, Vladimir G. 1954- Quantum invariants of knots and 3-manifolds De Gruyter Studies in Mathematics Knotentheorie (DE-588)4164318-5 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Topologie (DE-588)4060425-1 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Knoten Mathematik (DE-588)4164314-8 gnd Monoidale Kategorie (DE-588)4170466-6 gnd Topologische Invariante (DE-588)4310559-2 gnd Dimension 3 (DE-588)4321722-9 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd
subject_GND	(DE-588)4164318-5 (DE-588)4185712-4 (DE-588)4060425-1 (DE-588)4037379-4 (DE-588)4164314-8 (DE-588)4170466-6 (DE-588)4310559-2 (DE-588)4321722-9 (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_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	Knotentheorie (DE-588)4164318-5 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Topologie (DE-588)4060425-1 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Knoten Mathematik (DE-588)4164314-8 gnd Monoidale Kategorie (DE-588)4170466-6 gnd Topologische Invariante (DE-588)4310559-2 gnd Dimension 3 (DE-588)4321722-9 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd
topic_facet	Knotentheorie Topologische Mannigfaltigkeit Topologie Mannigfaltigkeit Knoten Mathematik Monoidale Kategorie Topologische Invariante Dimension 3 Quantenfeldtheorie
url	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110442663&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029107156&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000005407
work_keys_str_mv	AT turaevvladimirg quantuminvariantsofknotsand3manifolds AT walterdegruytergmbhcokg quantuminvariantsofknotsand3manifolds

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