Why are braids orderable?:
Gespeichert in:
| Späterer Titel: | Dehorney, Patrick Ordering Braids |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Paris
Soc. Math. de France
2002
|
| Schriftenreihe: | Panoramas et synthèses
14 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 190 S. |
| ISBN: | 285629135X |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV017285307 | ||
| 003 | DE-604 | ||
| 005 | 20230830 | ||
| 007 | t | ||
| 008 | 030704s2002 |||| 00||| eng d | ||
| 020 | |a 285629135X |9 2-85629-135-X | ||
| 035 | |a (OCoLC)53158258 | ||
| 035 | |a (DE-599)BVBBV017285307 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-739 |a DE-703 |a DE-29T | ||
| 050 | 0 | |a QA612.23 | |
| 082 | 0 | |a 514/.224 |2 22 | |
| 084 | |a SK 260 |0 (DE-625)143227: |2 rvk | ||
| 084 | |a SK 300 |0 (DE-625)143230: |2 rvk | ||
| 245 | 1 | 0 | |a Why are braids orderable? |c Patrick Dehornoy ... |
| 264 | 1 | |a Paris |b Soc. Math. de France |c 2002 | |
| 300 | |a XIII, 190 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Panoramas et synthèses |v 14 | |
| 650 | 7 | |a Relation d'ordre total |2 rasuqam | |
| 650 | 7 | |a Théorie des tresses |2 rasuqam | |
| 650 | 4 | |a Braid theory | |
| 650 | 4 | |a Linear orderings | |
| 650 | 0 | 7 | |a Zopf |g Mathematik |0 (DE-588)4191043-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ordnung |g Mathematik |0 (DE-588)4043745-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Zopf |g Mathematik |0 (DE-588)4191043-6 |D s |
| 689 | 0 | 1 | |a Ordnung |g Mathematik |0 (DE-588)4043745-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Dehornoy, Patrick |d 1952-2019 |e Sonstige |0 (DE-588)113599625 |4 oth | |
| 785 | 0 | 0 | |i Fortgesetzt durch |a Dehorney, Patrick |t Ordering Braids |d Providence, Rhode Island : American Mathematical Society, 2008 |z 978-0-8218-4431-1 |
| 830 | 0 | |a Panoramas et synthèses |v 14 |w (DE-604)BV037491878 |9 14 | |
| 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=010417704&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-010417704 | ||
Datensatz im Suchindex
| _version_ | 1804130129167777792 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author_GND | (DE-588)113599625 |
| building | Verbundindex |
| bvnumber | BV017285307 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612.23 |
| callnumber-search | QA612.23 |
| callnumber-sort | QA 3612.23 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 260 SK 300 |
| ctrlnum | (OCoLC)53158258 (DE-599)BVBBV017285307 |
| dewey-full | 514/.224 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.224 |
| dewey-search | 514/.224 |
| 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>01830nam a2200457 cb4500</leader><controlfield tag="001">BV017285307</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230830 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">030704s2002 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">285629135X</subfield><subfield code="9">2-85629-135-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)53158258</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV017285307</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-29T</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA612.23</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">514/.224</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 260</subfield><subfield code="0">(DE-625)143227:</subfield><subfield code="2">rvk</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="245" ind1="1" ind2="0"><subfield code="a">Why are braids orderable?</subfield><subfield code="c">Patrick Dehornoy ...</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Paris</subfield><subfield code="b">Soc. Math. de France</subfield><subfield code="c">2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 190 S.</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="490" ind1="1" ind2=" "><subfield code="a">Panoramas et synthèses</subfield><subfield code="v">14</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Relation d'ordre total</subfield><subfield code="2">rasuqam</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Théorie des tresses</subfield><subfield code="2">rasuqam</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Braid theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Linear orderings</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zopf</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4191043-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ordnung</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4043745-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Zopf</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4191043-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Ordnung</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4043745-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Dehornoy, Patrick</subfield><subfield code="d">1952-2019</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)113599625</subfield><subfield code="4">oth</subfield></datafield><datafield tag="785" ind1="0" ind2="0"><subfield code="i">Fortgesetzt durch</subfield><subfield code="a">Dehorney, Patrick</subfield><subfield code="t">Ordering Braids</subfield><subfield code="d">Providence, Rhode Island : American Mathematical Society, 2008</subfield><subfield code="z">978-0-8218-4431-1</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Panoramas et synthèses</subfield><subfield code="v">14</subfield><subfield code="w">(DE-604)BV037491878</subfield><subfield code="9">14</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=010417704&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:BVB01-010417704</subfield></datafield></record></collection> |
| 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 |
| oclc_num | 53158258 |
| open_access_boolean | |
| owner | DE-384 DE-739 DE-703 DE-29T |
| owner_facet | DE-384 DE-739 DE-703 DE-29T |
| physical | XIII, 190 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Soc. Math. de France |
| record_format | marc |
| 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 |
| volume_link | (DE-604)BV037491878 |
| work_keys_str_mv | AT dehornoypatrick whyarebraidsorderable |