A survey of knot theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Japanese |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1996
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Japan. übers. |
| Beschreibung: | XXI, 420 S. graph. Darst. |
| ISBN: | 3764351241 0817651241 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV010789041 | ||
| 003 | DE-604 | ||
| 005 | 19970312 | ||
| 007 | t | ||
| 008 | 960603s1996 gw d||| |||| 00||| eng d | ||
| 016 | 7 | |a 94761530X |2 DE-101 | |
| 020 | |a 3764351241 |c (Basel ...) Gb. : DM 128.00, sfr 108.00, S 934.40 |9 3-7643-5124-1 | ||
| 020 | |a 0817651241 |c (Boston ...) Gb. |9 0-8176-5124-1 | ||
| 035 | |a (OCoLC)36292959 | ||
| 035 | |a (DE-599)BVBBV010789041 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 1 | |a eng |h jpn | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-355 |a DE-20 |a DE-703 |a DE-91G |a DE-739 |a DE-12 |a DE-384 |a DE-19 |a DE-824 |a DE-706 |a DE-521 |a DE-634 |a DE-83 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA612.2.K39613 1996 | |
| 082 | 0 | |a 514/.224 |2 21 | |
| 082 | 0 | |a 514/.224 21 | |
| 084 | |a SK 300 |0 (DE-625)143230: |2 rvk | ||
| 084 | |a 27 |2 sdnb | ||
| 084 | |a 57M25 |2 msc | ||
| 084 | |a MAT 572f |2 stub | ||
| 100 | 1 | |a Kawauchi, Akio |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Knot theory |
| 245 | 1 | 0 | |a A survey of knot theory |c Akio Kawauchi |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1996 | |
| 300 | |a XXI, 420 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Aus dem Japan. übers. | ||
| 650 | 7 | |a Noeuds, théorie des |2 ram | |
| 650 | 4 | |a Nud, Théorie du | |
| 650 | 4 | |a Knot theory | |
| 650 | 0 | 7 | |a Knotentheorie |0 (DE-588)4164318-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Knotentheorie |0 (DE-588)4164318-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007207249&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007207249 | ||
Datensatz im Suchindex
| _version_ | 1804125272734171136 |
|---|---|
| adam_text | Table of contents
Preface ix
A prelude to the study of knot theory xi
Notes on research conventions and notations xxi
Chapter 0 Fundamentals of knot theory
0.1 Spaces 1
0.2 Manifolds and submanifolds 2
0.3 Knots and links 4
Supplementary notes for Chapter 0 5
Chapter 1 Presentations
1.1 Regular presentations 7
1.2 Braid presentations 12
1.3 Bridge presentations 18
Supplementary notes for Chapter 1 19
Chapter 2 Standard examples
2.1 Two bridge links 21
2.2 Torus links 26
2.3 Pretzel links 27
Supplementary notes for Chapter 2 28
Chapter 3 Compositions and decompositions
3.1 Compositions of links 31
3.2 Decompositions of links 33
3.3 Definition of a tangle and examples 34
3.4 How to judge the non splittability of a link 36
3.5 How to judge the primeness of a link 38
3.6 How to judge the hyperbolicity of a link 41
3.7 Non triviality of a link 42
3.8 Conway mutation 43
Supplementary notes for Chapter 3 45
Chapter 4 Seifert surfaces I: a topological approach
4.1 Definition and existence of Seifert surfaces 47
4.2 The Murasugi sum 50
4.3 Sutured manifolds 53
Supplementary notes for Chapter 4 59
V
vi TABLE OF CONTENTS
Chapter 5 Seifert surfaces II: an algebraic approach
5.1 The Seifert matrix 61
5.2 S equivalence 63
5.3 Number theoretic invariants 65
5.4 The reduced link module 69
5.5 The homology of a branched cyclic covering manifold 70
Supplementary notes for Chapter 5 72
Chapter 6 The fundamental group
6.1 Link groups and link group systems 73
6.2 Presentations of a link group 78
6.3 Subgroups and quotient groups of a link group 83
Supplementary notes for Chapter 6 86
Chapter 7 Multi variable Alexander polynomials
7.1 The Alexander module 87
7.2 Invariants of a A module 91
7.3 Graded Alexander polynomials 93
7.4 Torres conditions 97
Supplementary notes for Chapter 7 98
Chapter 8 Jones type polynomials I: a topological approach
8.1 The Jones polynomial 99
8.2 The skein polynomial 103
8.3 The Q and Kauffman polynomials 106
8.4 Properties of the polynomial invariants 107
8.5 The skein polynomial via a state model Ill
Supplementary notes for Chapter 8 112
Chapter 9 Jones type polynomials II: an algebraic approach
9.1 Preliminaries from representation theory 113
9.2 Link invariants of trace type 115
9.3 The skein polynomial as a link invariant of trace type 116
9.4 The Temperley Lieb algebra 117
Supplementary notes for Chapter 9 119
Chapter 10 Symmetries
10.1 Periodic knots 121
10.2 Freely periodic knots 125
10.3 Invertible knots 127
10.4 Amphicheiral knots 128
10.5 Symmetries of a hyperbolic knot 129
10.6 The symmetry group 131
10.7 Canonical decompositions and symmetry 134
Supplementary notes for Chapter 10 140
TABLE OF CONTENTS vii
Chapter 11 Local transformations
11.1 Unknotting operations 141
11.2 Properties of X Gordian distance 146
11.3 Properties of A Gordian distance 148
11.4 Properties of ft Gordian distance 149
11.5 Estimation of the X unknotting number 150
11.6 Local transformations of links 151
Supplementary notes for Chapter 11 153
Chapter 12 Cobordisms
12.1 The knot cobordism group 155
12.2 The matrix cobordism group 156
12.3 Link cobordism 163
Supplementary notes for Chapter 12 169
Chapter 13 Two knots I: a topological approach
13.1 A normal form 171
13.2 Constructing 2 knots 177
13.3 Seifert hypersurfaces 179
13.4 Exteriors of 2 knots 180
13.5 Cyclic covering spaces 182
13.6 The fc invariant 183
13.7 Ribbon presentations 185
Supplementary notes for Chapter 13 187
Chapter 14 Two knots II: an algebraic approach
14.1 High dimensional knot groups 189
14.2 Ribbon 2 knot groups 193
14.3 Torsion elements and the deficiency of 2 knot groups 196
Supplementary notes for Chapter 14 199
Chapter 15 Knot theory of spatial graphs
15.1 Topology of molecules 201
15.2 Uses of the notion of equivalence 202
15.3 Uses of the notion of neighborhood equivalence 205
Supplementary notes for Chapter 15 208
Chapter 16 Vassiliev Gusarov invariants
16.1 Vassiliev Gusarov algebra 209
16.2 Vassiliev Gusarov invariants and Jones type polynomials 211
16.3 Kontsevich s iterated integral invariant 214
16.4 Numerical invariants not of Vassiliev Gusarov type 217
Supplementary notes for Chapter 16 219
viii TABLE OF CONTENTS
Appendix A The equivalence of several notions of link equivalence 221
Appendix B Covering spaces
B.I The fundamental group 225
B.2 Definitions and properties of covering spaces 226
B.3 The classification of covering spaces 228
BA Covering transformations and the monodromy map 229
B.5 Branched covering spaces 230
Appendix C Canonical decompositions of 3 manifolds
C. 1 The connected sum 233
C.2 Dehn s lemma and the loop and sphere theorems 234
C.3 The equivariant loop and sphere theorems 234
CA Haken manifolds 235
C.5 Seifert manifolds 236
C.6 The annulus and torus theorems and the
torus decomposition theorem 238
C.I Hyperbolic 3 manifolds 239
Appendix D Heegaard splittings and Dehn surgery descriptions
D. 1 Heegaard splittings 241
D.2 Dehn surgery descriptions 243
Appendix E The Blanchfield duality theorem 247
Appendix F Tables of data
F.O Comments on the data 253
F. 1 Knot diagrams 255
F.2 Type and symmetry 263
F.3 Knot invariants 270
FA Presentation matrices 277
F.5 Ribbon presentations 279
F.6 Skein and Kauffman polynomials 282
F.I Surface link diagrams 303
References 305
Index 415
|
| any_adam_object | 1 |
| author | Kawauchi, Akio |
| author_facet | Kawauchi, Akio |
| author_role | aut |
| author_sort | Kawauchi, Akio |
| author_variant | a k ak |
| building | Verbundindex |
| bvnumber | BV010789041 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612.2.K39613 1996 |
| callnumber-search | QA612.2.K39613 1996 |
| callnumber-sort | QA 3612.2 K39613 41996 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 300 |
| classification_tum | MAT 572f |
| ctrlnum | (OCoLC)36292959 (DE-599)BVBBV010789041 |
| dewey-full | 514/.224 514/.22421 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.224 514/.224 21 |
| dewey-search | 514/.224 514/.224 21 |
| dewey-sort | 3514 3224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01755nam a2200481 c 4500</leader><controlfield tag="001">BV010789041</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19970312 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">960603s1996 gw d||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">94761530X</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3764351241</subfield><subfield code="c">(Basel ...) Gb. : DM 128.00, sfr 108.00, S 934.40</subfield><subfield code="9">3-7643-5124-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0817651241</subfield><subfield code="c">(Boston ...) Gb.</subfield><subfield code="9">0-8176-5124-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)36292959</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010789041</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">jpn</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA612.2.K39613 1996</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">514/.224</subfield><subfield code="2">21</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">514/.224 21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 300</subfield><subfield code="0">(DE-625)143230:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">27</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">57M25</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 572f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kawauchi, Akio</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Knot theory</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A survey of knot theory</subfield><subfield code="c">Akio Kawauchi</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Basel [u.a.]</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXI, 420 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Aus dem Japan. übers.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Noeuds, théorie des</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nud, Théorie du</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Knot theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Knotentheorie</subfield><subfield code="0">(DE-588)4164318-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Knotentheorie</subfield><subfield code="0">(DE-588)4164318-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007207249&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007207249</subfield></datafield></record></collection> |
| id | DE-604.BV010789041 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:58:56Z |
| institution | BVB |
| isbn | 3764351241 0817651241 |
| language | English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007207249 |
| oclc_num | 36292959 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-20 DE-703 DE-91G DE-BY-TUM DE-739 DE-12 DE-384 DE-19 DE-BY-UBM DE-824 DE-706 DE-521 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-20 DE-703 DE-91G DE-BY-TUM DE-739 DE-12 DE-384 DE-19 DE-BY-UBM DE-824 DE-706 DE-521 DE-634 DE-83 DE-11 DE-188 |
| physical | XXI, 420 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Kawauchi, Akio Verfasser aut Knot theory A survey of knot theory Akio Kawauchi Basel [u.a.] Birkhäuser 1996 XXI, 420 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus dem Japan. übers. Noeuds, théorie des ram Nud, Théorie du Knotentheorie (DE-588)4164318-5 gnd rswk-swf Knotentheorie (DE-588)4164318-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007207249&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kawauchi, Akio A survey of knot theory Noeuds, théorie des ram Nud, Théorie du Knot theory Knotentheorie (DE-588)4164318-5 gnd |
| subject_GND | (DE-588)4164318-5 |
| title | A survey of knot theory |
| title_alt | Knot theory |
| title_auth | A survey of knot theory |
| title_exact_search | A survey of knot theory |
| title_full | A survey of knot theory Akio Kawauchi |
| title_fullStr | A survey of knot theory Akio Kawauchi |
| title_full_unstemmed | A survey of knot theory Akio Kawauchi |
| title_short | A survey of knot theory |
| title_sort | a survey of knot theory |
| topic | Noeuds, théorie des ram Nud, Théorie du Knot theory Knotentheorie (DE-588)4164318-5 gnd |
| topic_facet | Noeuds, théorie des Nud, Théorie du Knot theory Knotentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007207249&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kawauchiakio knottheory AT kawauchiakio asurveyofknottheory |