Knots:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
De Gruyter
2014
|
| Edition: | 3., fully revised and extended edition |
| Series: | De Gruyter Studies in Mathematics
5 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIII, 417 S. graph. Darst. |
| ISBN: | 9783110270747 9783110270792 |
Staff View
MARC
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| 245 | 1 | 0 | |a Knots |c Gerhard Burde ; Heiner Zieschang ; Michael Heusener |
| 250 | |a 3., fully revised and extended edition | ||
| 264 | 1 | |a Berlin [u.a.] |b De Gruyter |c 2014 | |
| 300 | |a XIII, 417 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 700 | 1 | |a Zieschang, Heiner |d 1936-2004 |e Verfasser |0 (DE-588)11564489X |4 aut | |
| 700 | 1 | |a Heusener, Michael |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1806326604258869248 |
|---|---|
| adam_text |
Contents
Knots and isotopies
1
l.A Knots
. 1
1
.B Equivalence of knots
. 4
l.C Knot projections
. 9
l.D Global geometric properties
. 12
l.E History and sources
. 14
l.F Exercises
. 14
Geometric concepts
16
2.A Geometric properties of projections
. 16
2.B
Seifert
surfaces and genus
. 19
2.C Companion knots and product knots
. 21
2.D Braids, bridges, plats
. 23
2.E Slice knots and algebraic knots
. 26
2.F History and sources
. 28
2.G Exercises
. 28
Knot groups
30
3.A Homology
. 30
3.B Wirtinger presentation
. 32
3.C Peripheral system
. 40
3.D Knots on handlebodies
. 44
3.E Torus knots
. 48
3.F Asphericity of the knot complement
. 50
3.G History and sources
. 51
3.H Exercises
. 52
4
Commutator subgroup of a knot group
54
4.
A Construction of cyclic coverings
. 54
4.B Structure of the commutator subgroup
. 57
4.C A lemma of Brown and Crowell
. 59
4.D Examples and applications
. 62
4.E Commutator subgroups of satellites
. 64
4,F History and sources
. 68
4.G Exercises
. 68
5
Fibered knots
71
5.A Fibration theorem
. 71
5.B Fibered knots
. 74
5.C Applications and examples
. 77
5.D History and sources
. 84
5.E Exercises
. 84
6
A characterization of torus knots
85
6-А
Results and sources
. 85
6.
В
An elementary proof of Theorem
6.1 . 88
6.C Remarks on the proof
. 93
6.
D
History and sources
. 96
6.E Exercises
. 96
7
Factorization of knots
97
7.A Composition of knots
. 97
7.B Uniqueness of the decomposition into prime knots: proof
. 102
7.C Fibered knots and decompositions
. 106
7.D History and sources
. 108
7.E Exercises
. 109
8
Cyclic coverings and Alexander invariants 111
8.A Alexander module
.
Ill
8.
В
Infinite cyclic coverings and Alexander modules
. 112
8.C Homological properties of Coo
. 119
8.D Alexander polynomials
. 122
8.E Finite cyclic coverings
. 132
8.F History and sources
. 137
8.G Exercises
. 137
9
Free differential calculus and Alexander matrices
140
9.A Regular coverings and homotopy chains
. 140
9.B Fox differential calculus
. 142
9.
С
Calculation of Alexander polynomials
. 144
9.D Alexander polynomials of links
. 149
9.E Alexander-Conway polynomial
. 152
9.F Finite cyclic coverings again
. 155
9.G History and sources
. 158
9.H Exercises
. 158
10
Braids
161
10.A The classification of braids
. 161
10.B Normal form and group structure
. 169
10.C Configuration spaces and braid groups
. 174
10.D Braids and links
. 179
10.E History and sources
. 188
10.F Exercises
. 189
11
Manifolds as branched coverings
191
1
1.A Alexander's theorem
. 191
11.
В
Branched coverings and Heegaard diagrams
. 197
11
,C History and sources
. 206
1
l.D Exercises
. 207
12
Montesinos
links
208
12.A Schubert's normal form of knots and links with two bridges
. 208
12.B 4-Plats
(Viergeflechte) . 213
12.C Alexander polynomial and genus of a knot with two bridges
. 218
12.
D
Classification of
Montesinos
links
. 222
12.E Symmetries of
Montesinos
links
. 230
12.
F
History and sources
. 236
12.G Exercises
. 236
13
Quadratic forms of a knot
238
13.A The quadratic form of a knot
. 238
13.
В
Computation of the quadratic form of a knot
. 247
13.C Alternating knots and links
. 253
13.
D
Comparison of different concepts and examples
. 258
13.Е
History and sources
.264
13.F Exercises
.264
14
Representations of knot groups
266
14.A Metabelian representations
.266
14.B Homomorphisms of
Φ
into the group of motions of the Euclidean
plane
.272
14.C Linkage in coverings
.279
14.D Periodic knots
.285
14.E History and sources
.297
14.F Exercises
.297
15
Knots, knot manifolds, and knot groups
301
15.A Examples
.301
15.
В
Property
Ρ
for special knots
.304
15.
С
Prime knots and their manifolds and groups
.315
15.D Groups of product knots
.329
15.E History and sources
.332
15.F Exercises
.333
16
Bridge number and companionship
334
16.A
Seifert
surfaces for satellites
.334
16.B Companions of order one
.337
16.C Bridge number and height functions
.339
16.D History and sources
.352
16.
E
Exercises
.352
17
The 2-variable skein polynomial
353
17.
A Construction of a trace function on
a
Hecke
algebra
. 353
17.B The HOMFLY-PT polynomial
. 359
17.C History and sources
. 364
17.
D
Exercises
. 364
A Algebraic theorems
365
В
Theorems of 3-dimensional topology
371
С
Table
375
C.I Table
.376
D
Knot projections
Οχ
-949 384
References
387
Author index
407
Glossary of Symbols
411
Index
413 |
| any_adam_object | 1 |
| author | Burde, Gerhard 1931- Zieschang, Heiner 1936-2004 Heusener, Michael |
| author_GND | (DE-588)143762907 (DE-588)11564489X |
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| author_role | aut aut aut |
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| dewey-full | 514.2242 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2242 |
| dewey-search | 514.2242 |
| dewey-sort | 3514.2242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3., fully revised and extended edition |
| format | Book |
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| id | DE-604.BV041476090 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T01:08:08Z |
| institution | BVB |
| isbn | 9783110270747 9783110270792 |
| language | English |
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| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter Studies in Mathematics |
| series2 | De Gruyter Studies in Mathematics |
| spelling | Burde, Gerhard 1931- Verfasser (DE-588)143762907 aut Knots Gerhard Burde ; Heiner Zieschang ; Michael Heusener 3., fully revised and extended edition Berlin [u.a.] De Gruyter 2014 XIII, 417 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematics 5 Knoten Mathematik (DE-588)4164314-8 gnd rswk-swf Knotentheorie (DE-588)4164318-5 gnd rswk-swf Knoten Mathematik (DE-588)4164314-8 s DE-604 Knotentheorie (DE-588)4164318-5 s 1\p DE-604 Zieschang, Heiner 1936-2004 Verfasser (DE-588)11564489X aut Heusener, Michael Verfasser aut Erscheint auch als Online-Ausgabe 978-3-11-027078-5 De Gruyter Studies in Mathematics 5 (DE-604)BV000005407 5 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4284924&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026922143&sequence=000002&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 | Burde, Gerhard 1931- Zieschang, Heiner 1936-2004 Heusener, Michael Knots De Gruyter Studies in Mathematics Knoten Mathematik (DE-588)4164314-8 gnd Knotentheorie (DE-588)4164318-5 gnd |
| subject_GND | (DE-588)4164314-8 (DE-588)4164318-5 |
| title | Knots |
| title_auth | Knots |
| title_exact_search | Knots |
| title_full | Knots Gerhard Burde ; Heiner Zieschang ; Michael Heusener |
| title_fullStr | Knots Gerhard Burde ; Heiner Zieschang ; Michael Heusener |
| title_full_unstemmed | Knots Gerhard Burde ; Heiner Zieschang ; Michael Heusener |
| title_short | Knots |
| title_sort | knots |
| topic | Knoten Mathematik (DE-588)4164314-8 gnd Knotentheorie (DE-588)4164318-5 gnd |
| topic_facet | Knoten Mathematik Knotentheorie |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4284924&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026922143&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT burdegerhard knots AT zieschangheiner knots AT heusenermichael knots |