Holdings: An invitation to knot theory

An invitation to knot theory: virtual and classical

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Bibliographic Details
Main Author:	Dye, Heather A. (Author)
Format:	Book
Language:	English
Published:	Boca Raton CRC Press [2016]
Series:	A Chapman & Hall book
Subjects:	Knot theory Knotentheorie Einführung
Online Access:	Inhaltsverzeichnis Inhaltsverzeichnis
Physical Description:	xxx, 256 Seiten Illustrationen, Diagramme
ISBN:	9781498701648

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MARC


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adam_text	Titel: An invitation to knot theory Autor: Dye, Henry Abel Jahr: 2016 Contents Section I Knots and crossings Chapter 1 ¦ Virtual knots and links 3 1.1 CURVES IN THE PLANE 3 1.2 VIRTUAL LINKS 7 1.3 ORIENTED VIRTUAL LINK DIAGRAMS 15 1.4 OPEN PROBLEMS AND PROJECTS 17 Chapter 2 ¦ Linking invariants 19 2.1 CONDITIONAL STATEMENTS 19 2.2 WRITHE AND LINKING NUMBER 23 2.3 DIFFERENCE NUMBER 27 2.4 CROSSING WEIGHT NUMBERS 28 2.5 OPEN PROBLEMS AND PROJECTS 33 Chapter 3 ¦ A multiverse of knots 35 3.1 FLAT AND FREE LINKS 35 3.2 WELDED, SINGULAR, AND PSEUDO KNOTS 43 3.3 NEW KNOT THEORIES 46 3.4 OPEN PROBLEMS AND PROJECTS 47 Chapter 4 ¦ Crossing invariants 49 4.1 CROSSING NUMBERS 49 4.2 UNKNOTTING NUMBERS 55 4.3 UNKNOTTING SEQUENCE NUMBERS 59 4.4 OPEN PROBLEMS AND PROJECTS 61 Chapter 5 ¦ Constructing knots 63 5.1 SYMMETRY 63 viii ¦ Contents 5.2 TANGLES, MUTATION, AND PERIODIC LINKS 67 5.3 PERIODIC LINKS AND SATELLITE KNOTS 72 5.4 OPEN PROBLEMS AND PROJECTS 74 Section II Knot polynomials Chapter 6 ¦ The bracket polynomial 79 6.1 THE NORMALIZED KAUFFMAN BRACKET POLYNOMIAL 79 6.2 THE STATE SUM 84 6.3 THE IMAGE OF THE f-POLYNOMIAL 86 6.4 OPEN PROBLEMS AND PROJECTS 92 Chapter 7 ¦ Surfaces 95 7.1 SURFACES 95 7.2 CONSTRUCTIONS OF VIRTUAL LINKS 104 7.3 GENUS OF A VIRTUAL LINK 109 7.4 OPEN PROBLEMS AND PROJECTS 112 Chapter 8 ¦ Bracket polynomial II 115 8.1 STATES AND THE BOUNDARY PROPERTY 115 8.2 PROPER STATES 121 8.3 DIAGRAMS WITH ONE VIRTUAL CROSSING 122 8.4 OPEN PROBLEMS AND PROJECTS 124 Chapter 9 ¦ The checkerboard framing 127 9.1 CHECKERBOARD FRAMINGS 127 9.2 CUT POINTS 133 9.3 EXTENDING THE THEOREM 135 9.4 OPEN PROBLEMS AND PROJECTS 138 Chapter 10» Modifications of the bracket polynomial 139 10.1 THE FLAT BRACKET 139 10.2 THE ARROW POLYNOMIAL 141 10.3 VASSILIEV INVARIANTS 150 10.4 OPEN PROBLEMS AND PROJECTS 153 Section III Algebraic structures Chapter 11 ¦ Quandles 157 Contents ¦ ix 11.1 TRICOLORING 157 11.2 QUANDLES 160 11.3 KNOT QUANDLES 163 11.4 OPEN PROBLEMS AND PROJECTS 167 Chapter 12 ¦ Knots and quandles_169 12.1 A LITTLE LINEAR ALGEBRA AND THE TREFOIL 169 12.2 THE DETERMINANT OF A KNOT 172 12.3 THE ALEXANDER POLYNOMIAL 180 12.4 THE FUNDAMENTAL GROUP 182 12.5 OPEN PROBLEMS AND PROJECTS 183 Chapter 13« Biquandles_185 13.1 THE BIQUANDLE STRUCTURE 185 13.2 THE GENERALIZED ALEXANDER POLYNOMIAL 190 13.3 OPEN PROBLEMS AND PROJECTS 196 Chapter 14» Gauss diagrams_199 14.1 GAUSS WORDS AND DIAGRAMS 199 14.2 PARITY AND PARITY INVARIANTS 205 14.3 CROSSING WEIGHT NUMBER 210 14.4 OPEN PROBLEMS AND PROJECTS 212 Chapter 15» Applications_213 15.1 QUANTUM COMPUTATION 213 15.2 TEXTILES 215 15.3 OPEN PROBLEMSAND PROJECTS 218 Appendix A-Tables 221 A.1 KNOT TABLES 222 A.2 KNOT INVARIANTS 231 Appendix B - References by chapter_239 B.1 CHAPTER 1 B.2 CHAPTER 2 239 240 X ¦ Contents B.3 CHAPTER 3 240 B.4 CHAPTER 4 241 B.5 CHAPTER 5 243 B.6 CHAPTER 6 244 B.7 CHAPTER 7 245 B.8 CHAPTER 8 245 B.9 CHAPTER 9 246 B.10 CHAPTER 10 246 B.11 CHAPTER 11 248 B.12 CHAPTER 12 249 B.13 CHAPTER 13 250 B.14 CHAPTER 14 250 B.15 CHAPTER 15 251 Index 253
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spelling	Dye, Heather A. Verfasser (DE-588)1102214302 aut An invitation to knot theory virtual and classical Heather A. Dye Boca Raton CRC Press [2016] © 2016 xxx, 256 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall book Knot theory Knotentheorie (DE-588)4164318-5 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Knotentheorie (DE-588)4164318-5 s DE-604 http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=6771259&custom_att_2=simple_viewer An invitation to knot theory Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029053104&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
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title	An invitation to knot theory virtual and classical
title_auth	An invitation to knot theory virtual and classical
title_exact_search	An invitation to knot theory virtual and classical
title_full	An invitation to knot theory virtual and classical Heather A. Dye
title_fullStr	An invitation to knot theory virtual and classical Heather A. Dye
title_full_unstemmed	An invitation to knot theory virtual and classical Heather A. Dye
title_short	An invitation to knot theory
title_sort	an invitation to knot theory virtual and classical
title_sub	virtual and classical
topic	Knot theory Knotentheorie (DE-588)4164318-5 gnd
topic_facet	Knot theory Knotentheorie Einführung
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