Topology and combinatorics of 3-manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1995
|
| Schriftenreihe: | Lecture notes in mathematics
1599 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 446 S. graph. Darst. |
| ISBN: | 3540590633 0387590633 |
Internformat
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| 100 | 1 | |a Johannson, Klaus |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Topology and combinatorics of 3-manifolds |c Klaus Johannson |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1995 | |
| 300 | |a XVIII, 446 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1599 | |
| 650 | 7 | |a Manifolds |2 gtt | |
| 650 | 4 | |a Variétés topologiques à 3 dimensions | |
| 650 | 4 | |a Three-manifolds (Topology) | |
| 650 | 0 | 7 | |a Kombinatorik |0 (DE-588)4031824-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mannigfaltigkeit |0 (DE-588)4037379-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dimension 3 |0 (DE-588)4321722-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1805082782695686144 |
|---|---|
| adam_text |
Contents
Introduction v
Chapter I. Handlebodies
§1. Standard Graphs and Meridian Systems 1
The Sliding Process 2
Whitehead Equivalence Classes 4
Standard Graphs and Dehn Twists 7
§2. The Disc Complex 10
§3. Homeomorphisms 14
The Mapping Class Group 14
The Conjugacy Problem 17
The Torsion Problem 17
The Fixpoint Problem 18
§4. Pseudo Anosov Homeomorphisms 23
§5. Branching Complexes 24
Chapter II. Relative Handlebodies
§6. Heegaard Diagrams 37
§7. Surfaces 42
Simplicity of Relative Handlebodies 42
Minimal Meridian Systems 45
Finiteness for Surfaces 54
§8. Homeomorphisms 59
Classification 59
Mapping Class Group 60
§9. Duality 64
Piping, Pseudo Piping and Pruning 64
Piping in Relative Handlebodies 65
Pseudo Piping and Essential Surfaces 68
The First Homology Group 74
Contents xv
The Second Homology Group 75
Duality in Relative Handlebodies 80
§10. Presentations for Surfaces 84
Marked Basis 84
Marked Basis and Surfaces 85
Presenting Essential Surfaces 87
§11. The Seifert Characteristic 94
Complexities 94
Estimates 96
Applications 105
Surface Systems 107
§12. Algorithms for Surfaces 110
Preliminaries 110
The Compression Process 111
Compression Complexity 114
Compression Map 116
Compression Lines 119
Isotopy of Surfaces 122
Boundary Parallelity 127
§13. The Haken Spectrum 130
Matrices for Labelled Discs 130
Matrices for Presentations 131
Spectral Equations and Arc Systems 132
Jsotopy Algorithm 134
Generating Surfaces 136
Basic Surfaces 138
Searching for Essential Surfaces HO
Enumerating Essential Surfaces 145
Chapter III. Generalized One Relator 3 Manifolds
§14. Good Pencils 148
§15. The Handle Addition Lemma (Absolute Form) 152
Preliminaries 152
The Separating Cast 152
The Non Separating Case 155
Heegaard Strings 160
§16. The Handle Addition Lemma (Relative Form) 162
xvi Contents
Admissible Heegaard Strings 162
Displacements 164
Displacements are Almost Essential 168
Tubular Cages 173
Relative Handle Addition Lemma 181
§17. Homotopy and Isotopy 184
Deformations of Generalized Heegaard Strings 184
Deformations into Free Faces 186
Deformations into Bound Faces 189
Deformations between Generalized Heegaard Strings 203
§18. The Mapping Class Group 212
Preliminaries 212
Heegaard Strings and Mapping Class Group 213
§19. Incompressibility 217
§20. The Compression Algorithm 221
§21. The Haken Spectrum 231
Heegaard Cylinders 231
Estimates 233
The Seifert Characteristic 236
The Haken Spectrum 237
§22. An Example 239
Chapter IV. N Relator 3 Manifolds
§23. The Handle Addition Lemma (General Case) 247
Strictly Normal Surfaces 248
Strictly Normal Positions 249
Slides Associated to Bad Arcs 251
The Handle Addition Lemma 254
Reducibility of Heegaard Graphs 256
Good Pencils 261
Estimates 262
Heegaard Cylinders 264
Deformations of Heegaard Graphs 267
§24. The Unknotting Theorem 269
Existence of Local Knots 269
Resolving Local Knots 271
§25. Distances for Heegaard Graphs 276
Contents xvii
Definitions 276
Pushing Heegaard Graphs 277
Embeddings of N Relator 3 Manifolds 278
The Reidemeister Singer Theorem 281
Chapter V. The Space of Heegaard Graphs
§26. Constructing Heegaard Graphs 289
Heegaard Graphs and Presentations 289
Equivalences for Heegaard Graphs 290
Presentations Associated to Heegaard Graphs 291
Turbulization for Heegaard Graphs 293
Exotic Heegaard Strings 296
Exponential Growth 306
§27. Haken Complexes and Heegaard Complexes 310
Haken 2 Complexes 310
Haken 2 Complexes Associated to a Hierarchy 312
Useful Haken 2 Complexes 313
Graphs and Haken Graphs 317
Heegaard 2 Complexes 329
Useful Heegaard 2 Complexes 330
§28. Short Companions for Haken Graphs 333
Short Companion Arcs 333
Heaps 335
Pseudo Arcs, Bundle Paths and Combs 338
Complexities for Haken Graphs 343
Short Companions for Haken Graphs 344
§29. Invariant Regions for Long Arc Sequences 359
Train Tracks 359
Webs for 1 Manifolds 360
Spliced Graphs 362
Mixing Factors and Invariant Surfaces 364
§30. The Universal Limit for Induced Haken Graphs 376
Base Length of Bundle Paths 376
Inessential Bundle Paths 382
Squares 385
a Dominated Heegaard 2 Complexes 388
§31. Finiteness for Heegaard Graphs 389
xviii Contents
Special Slides 389
Finiteness for Heegaard Graphs 390
Growth of the Tietze Spectrum 399
§32. Rigidity for Heegaard Graphs 401
Definition of Small p Reductions 401
Existence of Small p Reductions 402
Edge Paths and Trees 410
Equivalent Vertices and Small p Reductions 412
Normal Curves for Heegaard Graphs 411
The Rigidity Theorem 420
§33. Reidemeister Zieschang Problem 423
Equivalence Classes of Curves 423
Appendix. Computing Surfaces 427
Non Separating Surfaces 427
Separating Surfaces 427
References 436
Index 442 |
| any_adam_object | 1 |
| author | Johannson, Klaus |
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| discipline | Mathematik |
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| language | English |
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| spelling | Johannson, Klaus Verfasser aut Topology and combinatorics of 3-manifolds Klaus Johannson Berlin u.a. Springer 1995 XVIII, 446 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1599 Manifolds gtt Variétés topologiques à 3 dimensions Three-manifolds (Topology) Kombinatorik (DE-588)4031824-2 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Dimension 3 (DE-588)4321722-9 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s Topologie (DE-588)4060425-1 s DE-604 Kombinatorik (DE-588)4031824-2 s Lecture notes in mathematics 1599 (DE-604)BV000676446 1599 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006711112&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Johannson, Klaus Topology and combinatorics of 3-manifolds Lecture notes in mathematics Manifolds gtt Variétés topologiques à 3 dimensions Three-manifolds (Topology) Kombinatorik (DE-588)4031824-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 3 (DE-588)4321722-9 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4031824-2 (DE-588)4037379-4 (DE-588)4321722-9 (DE-588)4060425-1 |
| title | Topology and combinatorics of 3-manifolds |
| title_auth | Topology and combinatorics of 3-manifolds |
| title_exact_search | Topology and combinatorics of 3-manifolds |
| title_full | Topology and combinatorics of 3-manifolds Klaus Johannson |
| title_fullStr | Topology and combinatorics of 3-manifolds Klaus Johannson |
| title_full_unstemmed | Topology and combinatorics of 3-manifolds Klaus Johannson |
| title_short | Topology and combinatorics of 3-manifolds |
| title_sort | topology and combinatorics of 3 manifolds |
| topic | Manifolds gtt Variétés topologiques à 3 dimensions Three-manifolds (Topology) Kombinatorik (DE-588)4031824-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 3 (DE-588)4321722-9 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Manifolds Variétés topologiques à 3 dimensions Three-manifolds (Topology) Kombinatorik Mannigfaltigkeit Dimension 3 Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006711112&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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