Knots and links:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2004
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 328 S. Ill., graph. Darst. |
| ISBN: | 0521839475 0521548314 9780521839471 9780521548311 |
Internformat
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| 650 | 4 | |a Lien, Théorie du | |
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Datensatz im Suchindex
| _version_ | 1804133318179946496 |
|---|---|
| adam_text | KNOTS AND LINKS PETER R. CROMWELL CAMBRIDGE UNIVERSITY PRESS CONTENTS
PREFACE NOTATION 1 INTRODUCTION 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 2 A
2, 2, 2 2. 2, 2 1 2 3 4 5 6 ,7 8 9 10 .11 ,12 KNOTS DEFORMATION
POLYGONAL KNOTS SMOOTH KNOTS TORUS KNOTS FOURIER KNOTS AND LISSAJOUS
KNOTS TOPOLOGICAL SYMMETRIES LINKS INVARIANTS THE CREATION OF CATALOGUES
A TECHNICALITY EXERCISES L TOPOLOGIST S TOOLKIT .1 .2 .3 .4 .5 .6 THE
3-SPHERE MANIFOLDS ORIENTATION AND ORIENTABILITY SEPARATION AND BOUNDING
INNERMOST AND OUTERMOST SURFACES XI XV 1 1 3 5 8 9 11 13 16 20 21 24 29
31 32 34 35 36 38 38 VI CONTENTS 2.7 EULER CHARACTERISTIC AND GENUS 41
2.8 SURGERY 42 2.9 COMPRESSIBILITY 43 2.10 TRANSVERSE INTERSECTIONS AND
GENERAL POSITION 44 2.11 GRAPHS 45 2.12 THE COMBINATORIAL APPROACH 48
2.13 EXERCISES 50 51 51 51 53 56 57 62 64 66 72 76 4 CONSTRUCTIONS AND
DECOMPOSITIONS OF LINKS 78 4.1 UNIONS OF LINKS 78 4.2 SATELLITES AND
COMPANIONSHIP 78 4.3 FACTORISING LINKS 81 4.4 PRIME SATELLITES 83 4.5
UNIQUENESS OF FACTORISATION 85 4.6 THE PRODUCT OPERATION 88 4.7 LINK
INVARIANTS AND FACTORISATION 90 4.8 HYPERBOLIC LINKS 93 4.9 TANGLE
DECOMPOSITION 95 4.10 BRIDGE PRESENTATIONS 98 3 LINK 3.1 3.2 3.3 3.4 3.5
3.6 3.7 3.8 3.9 3.10 DIAGRAMS PICTURES OF LINKS PROJECTIONS DIAGRAMS
SOME FAMILIES OF LINKS CROSSING NUMBER INVARIANTS FROM ORIENTED DIAGRAMS
A WARNING ABOUT MINIMAL DIAGRAMS MOVES ON DIAGRAMS THE CLASSIFICATION
PROBLEM EXERCISES CONTENTS VII 4.11 EXERCISES 100 5 SPANNING SURFACES
AND GENUS 102 5.1 SEIFERT S ALGORITHM 102 5.2 SEIFERT GRAPHS 105 5.3
GENUS-1 KNOTS 106 5.4 DIFFERENT GENUS MEASURES 110 5.5 SURGERY
EQUIVALENCE 114 5.6 GENUS AND FACTORISATION 118 5.7 LINKING NUMBER
REVISITED 121 5.8 GENUS OF SATELLITES 124 5.9 EXERCISES 127 6 MATRIX
INVARIANTS 129 6.1 LOOPS IN GRAPHS 129 6.2 SIMPLICIAL COMPLEXES 132 6.3
LOOPS IN SIMPLICIAL COMPLEXES 133 6.4 HOMOLOGY OF SURFACES 137 6.5 THE
SEIFERT MATRIX 139 6.6 LINK INVARIANTS FROM THE SEIFERT MATRIX 142 6.7
PROPERTIES OF SIGNATURE AND DETERMINANT 145 6.8 SIGNATURE AND UNKNOTTING
NUMBER 151 6.9 EXERCISES 154 7 THE ALEXANDER-CONWAY POLYNOMIAL 157 7.1
THE ALEXANDER POLYNOMIAL 157 7.2 THE ALEXANDER POLYNOMIAL AND GENUS 161
7.3 THE ALEXANDER SKEIN RELATION 162 7.4 THE CONWAY POLYNOMIAL 163 7.5
RESOLVING TREES 167 7.6 HOMOGENEOUS LINKS 170 7.7 LINEAR SKEIN THEORY
174 VIII CONTENTS 7.8 MARKED TANGLES AND MUTATION 177 7.9 CONWAY S
FRACTION FORMULA 181 7.10 CYLINDRICAL TANGLES 183 7.11 A TROUBLESOME
PAIR 185 7.12 EXERCISES 186 8 RATIONAL TANGLES 189 8.1 GENERATING
RATIONAL TANGLES 189 8.2 CLASSIFICATION OF RATIONAL TANGLES 193 8.3
HOMOLOGY AND MAPS 196 8.4 AUTOMORPHISMS OF THE TORUS 198 8.5
REPRESENTING TANGLE OPERATIONS BY MATRICES 199 8.6 CONTINUED FRACTIONS
202 8.7 RATIONAL LINKS 205 8.8 ENUMERATING RATIONAL LINKS 209 8.9
APPLICATIONS OF RATIONAL TANGLES 211 8.10 EXERCISES 214 9 MORE
POLYNOMIALS 215 9.1 DISCOVERY OF THE JONES POLYNOMIAL 215 9.2 THE
KAUFFMAN BRACKET 217 9.3 PROPERTIES OF THE BRACKET POLYNOMIAL 221 9.4
STATES OF GRAPHS AND DIAGRAMS 224 9.5 ADEQUATE DIAGRAMS 229 9.6 BOUNDS
ON CROSSING NUMBER 235 9.7 POLYNOMIAL LINK INVARIANTS 236 9.8 EXERCISES
239 10 CLOSED BRAIDS AND ARC PRESENTATIONS 241 10.1 BRAID PRESENTATIONS
241 10.2 THE HOMFLY POLYNOMIAL 244 10.3 THE HOMFLY POLYNOMIAL AND BRAID
INDEX 247 CONTENTS IX 10.4 BRAID INDEX OF RATIONAL LINKS 10.5
CLASSIFICATION OF TORUS KNOTS 10.6 ARC PRESENTATIONS 10.7 ARC
PRESENTATIONS ON DIAGRAMS 10.8 ARC PRESENTATIONS FROM DIAGRAMS 10.9
BRAID PRESENTATIONS OF SATELLITES 10.10 APPLICATIONS OF THE OPEN-BOOK
INFRASTRUCTURE 10.11 EXERCISES APPENDIX A APPENDIX B APPENDIX C APPENDIX
D APPENDIX E APPENDIX F BIBLIOGRAPHY INDEX KNOT DIAGRAMS NUMERICAL
INVARIANTS PROPERTIES POLYNOMIALS POLYGON COORDINATES FAMILY PROPERTIES
249 253 256 261 266 272 280 284 286 294 297 300 306 307 308 323
|
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| dewey-full | 514/.2242 |
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| dewey-ones | 514 - Topology |
| dewey-raw | 514/.2242 |
| dewey-search | 514/.2242 |
| dewey-sort | 3514 42242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV019817100 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:06:48Z |
| institution | BVB |
| isbn | 0521839475 0521548314 9780521839471 9780521548311 |
| language | English |
| lccn | 2004045914 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013142423 |
| oclc_num | 60346793 |
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| physical | XVII, 328 S. Ill., graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Cromwell, Peter R. Verfasser aut Knots and links Peter R. Cromwell 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2004 XVII, 328 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lien, Théorie du Nuds, Théorie des aKnot theory aLink theory Verschlingung (DE-588)4191540-9 gnd rswk-swf Knoten Mathematik (DE-588)4164314-8 gnd rswk-swf Knoten Mathematik (DE-588)4164314-8 s Verschlingung (DE-588)4191540-9 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013142423&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cromwell, Peter R. Knots and links Lien, Théorie du Nuds, Théorie des aKnot theory aLink theory Verschlingung (DE-588)4191540-9 gnd Knoten Mathematik (DE-588)4164314-8 gnd |
| subject_GND | (DE-588)4191540-9 (DE-588)4164314-8 |
| title | Knots and links |
| title_auth | Knots and links |
| title_exact_search | Knots and links |
| title_full | Knots and links Peter R. Cromwell |
| title_fullStr | Knots and links Peter R. Cromwell |
| title_full_unstemmed | Knots and links Peter R. Cromwell |
| title_short | Knots and links |
| title_sort | knots and links |
| topic | Lien, Théorie du Nuds, Théorie des aKnot theory aLink theory Verschlingung (DE-588)4191540-9 gnd Knoten Mathematik (DE-588)4164314-8 gnd |
| topic_facet | Lien, Théorie du Nuds, Théorie des aKnot theory aLink theory Verschlingung Knoten Mathematik |
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