Why are braids orderable?:
Saved in:
| New Title: | Dehorney, Patrick Ordering Braids |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Paris
Soc. Math. de France
2002
|
| Series: | Panoramas et synthèses
14 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 190 S. |
| ISBN: | 285629135X |
Staff View
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Record in the Search Index
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| adam_text | Titel: Why are braids orderable?
Autor: Dehornoy, Patrick
Jahr: 2002
CONTENTS
Introduction .................................................................. vii
An idea whose time was overdue............................................. vii
The importance of being orderable ........................................... ix
Organization of the text ..................................................... x
Guidelines to the reader ..................................................... xii
1. A linear ordering of braids ............................................... 1
1.1. Braid groups ............................................................ 1
1.2. A linear ordering on Bn ................................................. 7
1.3. Applications ............................................................. 17
2. Self-distributivity ......................................................... 23
2.1. The action of braids on LD-systems ..................................... 24
2.2. Special braids ........................................................... 34
2.3. The group of left self-distributivity ...................................... 40
2.4. Normal forms in free LD-systems ........................................ 49
2.5. Appendix: Iterations of elementary embeddings in set theory ........... 51
3. Handle reduction .......................................................... 55
3.1. Handles .................................................................. 55
3.2. Convergence of handle reduction ........................................ 57
3.3. Implementations and variants ........................................... 66
4. Finite trees ................................................................ 69
4.1. Encoding positive braid words in trees .................................. 70
4.2. A well-ordering on positive braid words ................................. 73
4.3. Reduction of positive braid words ....................................... 76
4.4. Applications ............................................................. 85
5. Automorphisms of a free group ......................................... 91
5.1. Keeping track of the letters .............................................. 91
5.2. From an automorphism back to a braid ................................. 97
CONTENTS
6. Curve diagrams ...........................................................101
6.1. Mapping class groups and curve diagrams ...............................101
6.2. A braid ordering using curve diagrams ..................................103
6.3. Generalizations ..........................................................109
7. Hyperbolic geometry .....................................................Ill
7.1. Uncountably many orderings of the braid group .........................Ill
7.2. The classification of orderings induced by the action on R ...............121
7.3. A proof of Property S for all Thurston-type orderings ...................128
7.4. A combinatorial approach and an extension to Bx ......................129
8. Triangulations .............................................................133
8.1. Singular triangulations ..................................................134
8.2. The Mosher normal form ................................................140
8.3. Laminations .............................................................148
8.4. Integral laminations .....................................................150
8.5. Action of the braid group on laminations ................................152
9. Bi-ordering the pure braid groups ......................................159
9.1. Descending central series ................................................159
9.2. An effective ordering onP? ..............................................160
9.3. Incompatibility of the orderings: local indicability .......................166
10. Open questions ...........................................................169
10.1. Well-ordering on positive braids ........................................169
10.2. Finding cr-positive representatives ......................................171
10.3. Topology of the space of orderings ......................................173
10.4. Generalizations and extensions .........................................174
Bibliography ..................................................................177
Index ..........................................................................187
Index of Notation ............................................................189
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| id | DE-604.BV017285307 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:16:07Z |
| institution | BVB |
| isbn | 285629135X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010417704 |
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| physical | XIII, 190 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Soc. Math. de France |
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| series | Panoramas et synthèses |
| series2 | Panoramas et synthèses |
| spelling | Why are braids orderable? Patrick Dehornoy ... Paris Soc. Math. de France 2002 XIII, 190 S. txt rdacontent n rdamedia nc rdacarrier Panoramas et synthèses 14 Relation d'ordre total rasuqam Théorie des tresses rasuqam Braid theory Linear orderings Zopf Mathematik (DE-588)4191043-6 gnd rswk-swf Ordnung Mathematik (DE-588)4043745-0 gnd rswk-swf Zopf Mathematik (DE-588)4191043-6 s Ordnung Mathematik (DE-588)4043745-0 s DE-604 Dehornoy, Patrick 1952-2019 Sonstige (DE-588)113599625 oth Fortgesetzt durch Dehorney, Patrick Ordering Braids Providence, Rhode Island : American Mathematical Society, 2008 978-0-8218-4431-1 Panoramas et synthèses 14 (DE-604)BV037491878 14 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010417704&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Why are braids orderable? Panoramas et synthèses Relation d'ordre total rasuqam Théorie des tresses rasuqam Braid theory Linear orderings Zopf Mathematik (DE-588)4191043-6 gnd Ordnung Mathematik (DE-588)4043745-0 gnd |
| subject_GND | (DE-588)4191043-6 (DE-588)4043745-0 |
| title | Why are braids orderable? |
| title_auth | Why are braids orderable? |
| title_exact_search | Why are braids orderable? |
| title_full | Why are braids orderable? Patrick Dehornoy ... |
| title_fullStr | Why are braids orderable? Patrick Dehornoy ... |
| title_full_unstemmed | Why are braids orderable? Patrick Dehornoy ... |
| title_new | Dehorney, Patrick Ordering Braids |
| title_short | Why are braids orderable? |
| title_sort | why are braids orderable |
| topic | Relation d'ordre total rasuqam Théorie des tresses rasuqam Braid theory Linear orderings Zopf Mathematik (DE-588)4191043-6 gnd Ordnung Mathematik (DE-588)4043745-0 gnd |
| topic_facet | Relation d'ordre total Théorie des tresses Braid theory Linear orderings Zopf Mathematik Ordnung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010417704&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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