Braids and self-distributivity:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2000
|
| Schriftenreihe: | Progress in mathematics
192 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XIX, 623 S. graph. Darst. |
| ISBN: | 9783764363437 3764363436 |
Internformat
MARC
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| 245 | 1 | 0 | |a Braids and self-distributivity |c Patrick Dehornoy |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2000 | |
| 300 | |a XIX, 623 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 192 | |
| 500 | |a Literaturangaben | ||
| 650 | 4 | |a Ensembles, Théorie des | |
| 650 | 4 | |a Tresses, Théorie des | |
| 650 | 4 | |a Braid theory | |
| 650 | 4 | |a Set theory | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009007552 | ||
Datensatz im Suchindex
| _version_ | 1804127976477949952 |
|---|---|
| adam_text | Contents
Preface xi
Part A: Ordering the Braids
I. Braids vs. Self Distributive Systems 1
1.1 Braid Groups 4
1.2 Braid Colourings 13
1.3 A Self Distributive Operation on Braids 26
1.4 Extended Braids 35
1.5 Notes 44
II. Word Reversing 47
II. 1 Complemented Presentations 48
11.2 Coherent Complements 58
11.3 Garside Elements 68
11.4 The Case of Braids 78
11.5 Double Reversing 87
11.6 Notes 94
III. The Braid Order 97
111.1 More about Braid Colourings 98
111.2 The Linear Ordering of Braids 106
111.3 Handle Reduction 115
111.4 Alternative Definitions 127
111.5 Notes 137
Contents
IV. The Order on Positive Braids 141
IV.l The Case of Three Strands 142
IV.2 The General Case 150
IV.3 Applications 165
IV.4 Notes 170
IV.Appendix: Rank Tables 172
Part B: Free LD systems
V. Orders on Free LD systems 175
V.I Free Systems 178
V.2 The Absorption Property 186
V.3 The Confluence Property 193
V.4 The Comparison Property 200
V.5 Canonical Orders 209
V.6 Applications 216
V.7 Notes 231
VI. Normal Forms 235
VI. 1 Terms as Trees 236
VI.2 The Cuts of a Term 242
VI.3 The 9 Normal Form 250
VI.4 The Right Normal Form 256
VI.5 Applications 271
VI.6 Notes 276
VI.Appendix: The First Codes 280
VII. The Geometry Monoid 285
VII. 1 Left Self Distributivity Operators 286
VII.2 Relations in the Geometry Monoid 301
VII.3 Syntactic Proofs 310
VII.4 Cuts and Collapsing 322
VII.5 Notes 329
Contents
VIII. The Group of Left Self Distributivity 331
VIII. 1 The Group GLD and the Monoid MLD 332
VIII.2 The Blueprint of a Term 343
VIII.3 Order Properties in GLD 356
VIII.4 Parabolic Subgroups 367
VIII.5 Simple Elements in MLD 371
VIII.6 Notes 383
IX. Progressive Expansions 385
IX.l The Polish Algorithm 386
IX.2 The Content of a Term 395
IX.3 Perfect Terms 401
IX.4 Convergence Results 415
IX. 5 Effective Decompositions 421
IX.6 The Embedding Conjecture 428
IX.7 Notes 436
IX.Appendix: Other Algebraic Identities 439
Part C: Other LD Systems
X. More LD Systems 443
X.I The Laver Tables 446
X.2 Finite Monogenic LD systems 457
X.3 Multi LD Systems 467
X.4 Idempotent LD systems 472
X.5 Two Sided Self Distributivity 476
X.6 Notes 480
X.Appendix: The First Laver Tables 485
XL LD Monoids 489
XI.l LD Monoids 490
XI. 2 Completion of an LD System 498
XI.3 Free LD Monoids 5U
XI.4 Orders on Free LD Monoids 517
XI.5 Extended Braids 527
XI.6 Notes 534
Contents
XII. Elementary Embeddings 537
XII.l Large Cardinals 538
XII.2 Elementary Embeddings 546
XII.3 Operations on Elementary Embeddings 553
XII.4 Finite Quotients 559
XII.5 Notes 568
XIII. More about the Laver Tables 571
XIII. 1 A Dictionary 572
XIII.2 Computation of Rows 577
XIII.3 Fast Growing Functions 583
XIII.4 Lower Bounds 591
XIII.5 Notes 598
Bibliography 603
List of Symbols 615
Index 619
|
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| author | Dehornoy, Patrick 1952-2019 |
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| ctrlnum | (OCoLC)44461864 (DE-599)BVBBV013219056 |
| 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 |
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| id | DE-604.BV013219056 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:41:54Z |
| institution | BVB |
| isbn | 9783764363437 3764363436 |
| language | English |
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| owner_facet | DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-11 |
| physical | XIX, 623 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Dehornoy, Patrick 1952-2019 Verfasser (DE-588)113599625 aut Braids and self-distributivity Patrick Dehornoy Basel [u.a.] Birkhäuser 2000 XIX, 623 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 192 Literaturangaben Ensembles, Théorie des Tresses, Théorie des Braid theory Set theory Gruppoid (DE-588)4158484-3 gnd rswk-swf Zopfgruppe (DE-588)4225944-7 gnd rswk-swf Wortproblem (DE-588)4337256-9 gnd rswk-swf Zopfgruppe (DE-588)4225944-7 s Gruppoid (DE-588)4158484-3 s Wortproblem (DE-588)4337256-9 s DE-604 Progress in mathematics 192 (DE-604)BV000004120 192 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009007552&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dehornoy, Patrick 1952-2019 Braids and self-distributivity Progress in mathematics Ensembles, Théorie des Tresses, Théorie des Braid theory Set theory Gruppoid (DE-588)4158484-3 gnd Zopfgruppe (DE-588)4225944-7 gnd Wortproblem (DE-588)4337256-9 gnd |
| subject_GND | (DE-588)4158484-3 (DE-588)4225944-7 (DE-588)4337256-9 |
| title | Braids and self-distributivity |
| title_auth | Braids and self-distributivity |
| title_exact_search | Braids and self-distributivity |
| title_full | Braids and self-distributivity Patrick Dehornoy |
| title_fullStr | Braids and self-distributivity Patrick Dehornoy |
| title_full_unstemmed | Braids and self-distributivity Patrick Dehornoy |
| title_short | Braids and self-distributivity |
| title_sort | braids and self distributivity |
| topic | Ensembles, Théorie des Tresses, Théorie des Braid theory Set theory Gruppoid (DE-588)4158484-3 gnd Zopfgruppe (DE-588)4225944-7 gnd Wortproblem (DE-588)4337256-9 gnd |
| topic_facet | Ensembles, Théorie des Tresses, Théorie des Braid theory Set theory Gruppoid Zopfgruppe Wortproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009007552&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT dehornoypatrick braidsandselfdistributivity |