Braid groups:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2008
|
| Series: | Graduate texts in mathematics
247 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 340 S. graph. Darst. |
| ISBN: | 9780387338415 9780387685489 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
v
1
Braids and Braid Groups
.................................. 1
1.1
The
Artin
braid groups
.................................. 1
1.2
Braids and braid diagrams
................................ 4
1.3
Pure braid groups
....................................... 18
1.4
Configuration spaces
..................................... 25
1.5
Braid automorphisms of free groups
........................ 31
1.6
Braids and homeomorphisms
.............................. 35
1.7
Groups of homeomorphisms vs. configuration spaces
......... 40
Notes
....................................................... 45
2
Braids, Knots, and Links
.................................. 47
2.1
Knots and links in three-dimensional manifolds
.............. 47
2.2
Closed braids in the solid torus
............................ 51
2.3
Alexander s theorem
..................................... 58
2.4
Links as closures of braids: an algorithm
.................... 61
2.5
Markov s theorem
....................................... 67
2.6
Deduction of Markov s theorem from Lemma
2.11........... 71
2.7
Proof of Lemma
2.11..................................... 83
Notes
....................................................... 91
3
Homological Representations of the Braid Groups
......... 93
3.1
The
Burau
representation
................................ 93
3.2
Nonfaithfulness of the
Burau
representation
................. 98
3.3
The reduced
Burau
representation
.........................107
3.4
The Alexander-Conway polynomial of links
.................
Ill
3.5
The Lawrence-Krammer-Bigelow representation
............118
3.6
Noodles vs. spanning arcs
................................125
3.7
Proof of Theorem
3.15...................................137
Notes
.......................................................149
χ
Contents
4 Symmetrie
Groups and Iwahori-Hecke Algebras
...........151
4.1
The symmetric groups
...................................151
4.2
The Iwahori-Hecke algebras
..............................163
4.3
The Ocneanu traces
.....................................170
4.4
The Jones-Conway polynomial
............................173
4.5 Semisimple
algebras and modules
..........................175
4.6
Semisimplicity of the Iwahori-Hecke algebras
...............191
Notes
.......................................................193
5
Representations of the Iwahori-Hecke Algebras
............195
5.1
The combinatorics of partitions and tableaux
...............195
5.2
The Young lattice
.......................................200
5.3 Seminormal
representations
...............................207
5.4
Proof of Theorem
5.11...................................210
5.5
Simplicity of the
seminormal
representations
................215
5.6
Simplicity of the reduced
Burau
representation
..............219
5.7
The Temperley-Lieb algebras
.............................222
Notes
.......................................................236
6
Garside Monoids and Braid Monoids
......................239
6.1
Monoids
................................................239
6.2
Normal forms and the conjugacy problem
...................243
6.3
Groups of fractions and pre-Garside monoids
................251
6.4
Garside monoids
........................................255
6.5
The braid monoid
.......................................259
6.6
Generalized braid groups
.................................266
Notes
.......................................................272
7
An Order on the Braid Groups
............................273
7.1
Orderable groups
........................................273
7.2
Pure braid groups are biorderable
.........................278
7.3
The Dehornoy order
.....................................282
7.4
Nontriviality of
σ
-positive
braids
..........................287
7.5
Handle reduction
........................................291
7.6
The Nielsen-Thurston approach
...........................307
Notes
.......................................................309
A Presentations of SL2(Z) and PSL2(Z)
......................311
Notes
.......................................................314
8
Fibrations and Homotopy Sequences
.......................315
С
The Birman-Murakami-Wenzl Algebras
...................317
Contents xi
D
Left Self-Distributive Sets
.................................321
D.I LD sets, racks, and quandles
..............................321
D.2 An action of the braid monoid
............................322
D.3 Orderable LD sets
.......................................323
Notes
.......................................................325
References
.....................................................327
Index
..........................................................337
|
| adam_txt |
Contents
Preface
v
1
Braids and Braid Groups
. 1
1.1
The
Artin
braid groups
. 1
1.2
Braids and braid diagrams
. 4
1.3
Pure braid groups
. 18
1.4
Configuration spaces
. 25
1.5
Braid automorphisms of free groups
. 31
1.6
Braids and homeomorphisms
. 35
1.7
Groups of homeomorphisms vs. configuration spaces
. 40
Notes
. 45
2
Braids, Knots, and Links
. 47
2.1
Knots and links in three-dimensional manifolds
. 47
2.2
Closed braids in the solid torus
. 51
2.3
Alexander's theorem
. 58
2.4
Links as closures of braids: an algorithm
. 61
2.5
Markov's theorem
. 67
2.6
Deduction of Markov's theorem from Lemma
2.11. 71
2.7
Proof of Lemma
2.11. 83
Notes
. 91
3
Homological Representations of the Braid Groups
. 93
3.1
The
Burau
representation
. 93
3.2
Nonfaithfulness of the
Burau
representation
. 98
3.3
The reduced
Burau
representation
.107
3.4
The Alexander-Conway polynomial of links
.
Ill
3.5
The Lawrence-Krammer-Bigelow representation
.118
3.6
Noodles vs. spanning arcs
.125
3.7
Proof of Theorem
3.15.137
Notes
.149
χ
Contents
4 Symmetrie
Groups and Iwahori-Hecke Algebras
.151
4.1
The symmetric groups
.151
4.2
The Iwahori-Hecke algebras
.163
4.3
The Ocneanu traces
.170
4.4
The Jones-Conway polynomial
.173
4.5 Semisimple
algebras and modules
.175
4.6
Semisimplicity of the Iwahori-Hecke algebras
.191
Notes
.193
5
Representations of the Iwahori-Hecke Algebras
.195
5.1
The combinatorics of partitions and tableaux
.195
5.2
The Young lattice
.200
5.3 Seminormal
representations
.207
5.4
Proof of Theorem
5.11.210
5.5
Simplicity of the
seminormal
representations
.215
5.6
Simplicity of the reduced
Burau
representation
.219
5.7
The Temperley-Lieb algebras
.222
Notes
.236
6
Garside Monoids and Braid Monoids
.239
6.1
Monoids
.239
6.2
Normal forms and the conjugacy problem
.243
6.3
Groups of fractions and pre-Garside monoids
.251
6.4
Garside monoids
.255
6.5
The braid monoid
.259
6.6
Generalized braid groups
.266
Notes
.272
7
An Order on the Braid Groups
.273
7.1
Orderable groups
.273
7.2
Pure braid groups are biorderable
.278
7.3
The Dehornoy order
.282
7.4
Nontriviality of
σ
-positive
braids
.287
7.5
Handle reduction
.291
7.6
The Nielsen-Thurston approach
.307
Notes
.309
A Presentations of SL2(Z) and PSL2(Z)
.311
Notes
.314
8
Fibrations and Homotopy Sequences
.315
С
The Birman-Murakami-Wenzl Algebras
.317
Contents xi
D
Left Self-Distributive Sets
.321
D.I LD sets, racks, and quandles
.321
D.2 An action of the braid monoid
.322
D.3 Orderable LD sets
.323
Notes
.325
References
.327
Index
.337 |
| any_adam_object | 1 |
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| author | Kassel, Christian Turaev, Vladimir G. 1954- |
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| dewey-ones | 514 - Topology |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV035032549 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:50:20Z |
| indexdate | 2024-07-09T21:20:39Z |
| institution | BVB |
| isbn | 9780387338415 9780387685489 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016701511 |
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| physical | XI, 340 S. graph. Darst. |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Kassel, Christian Verfasser aut Braid groups Christian Kassel ; Vladimir Turaev New York, NY Springer 2008 XI, 340 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 247 Zopfgruppe (DE-588)4225944-7 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Zopfgruppe (DE-588)4225944-7 s DE-604 Turaev, Vladimir G. 1954- Verfasser (DE-588)122717791 aut Graduate texts in mathematics 247 (DE-604)BV000000067 247 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016701511&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kassel, Christian Turaev, Vladimir G. 1954- Braid groups Graduate texts in mathematics Zopfgruppe (DE-588)4225944-7 gnd |
| subject_GND | (DE-588)4225944-7 (DE-588)4151278-9 |
| title | Braid groups |
| title_auth | Braid groups |
| title_exact_search | Braid groups |
| title_exact_search_txtP | Braid groups |
| title_full | Braid groups Christian Kassel ; Vladimir Turaev |
| title_fullStr | Braid groups Christian Kassel ; Vladimir Turaev |
| title_full_unstemmed | Braid groups Christian Kassel ; Vladimir Turaev |
| title_short | Braid groups |
| title_sort | braid groups |
| topic | Zopfgruppe (DE-588)4225944-7 gnd |
| topic_facet | Zopfgruppe Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016701511&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT kasselchristian braidgroups AT turaevvladimirg braidgroups |