Introduction to 3-manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Society
2014
|
| Schriftenreihe: | Graduate studies in mathematics
151 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | X, 286 S. graph. Darst. |
| ISBN: | 9781470410209 |
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| 245 | 1 | 0 | |a Introduction to 3-manifolds |c Jennifer Schultens |
| 246 | 1 | 3 | |a Introduction to three-manifolds |
| 264 | 1 | |a Providence, RI |b American Math. Society |c 2014 | |
| 300 | |a X, 286 S. |b graph. Darst. | ||
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| 490 | 1 | |a Graduate studies in mathematics |v 151 | |
| 500 | |a Includes bibliographical references and index | ||
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| 650 | 7 | |a Manifolds and cell complexes ... Topological manifolds ... Topology of general $3$-manifolds |2 msc | |
| 650 | 7 | |a Manifolds and cell complexes ... Topological manifolds ... Geometric structures on manifolds |2 msc | |
| 650 | 7 | |a Manifolds and cell complexes ... Topological manifolds ... Neighborhoods of submanifolds |2 msc | |
| 650 | 7 | |a Manifolds and cell complexes ... Topological manifolds ... $S {n-1}subset E n$, Schoenflies problem |2 msc | |
| 650 | 7 | |a Manifolds and cell complexes ... Topological manifolds ... General position and transversality |2 msc | |
| 650 | 7 | |a Manifolds and cell complexes ... PL-topology ... Triangulating manifolds |2 msc | |
| 650 | 7 | |a Manifolds and cell complexes ... PL-topology ... Comparison of PL-structures: classification, Hauptvermutung |2 msc | |
| 650 | 7 | |a Manifolds and cell complexes ... PL-topology ... Regular neighborhoods |2 msc | |
| 650 | 7 | |a Manifolds and cell complexes ... PL-topology ... Knots and links (in high dimensions) |2 msc | |
| 650 | 4 | |a Topological manifolds | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Manifolds and cell complexes ... Topological manifolds ... Topology of $E 2$, $2$-manifolds | |
| 650 | 4 | |a Manifolds and cell complexes ... Topological manifolds ... Topology of general $3$-manifolds | |
| 650 | 4 | |a Manifolds and cell complexes ... Topological manifolds ... Geometric structures on manifolds | |
| 650 | 4 | |a Manifolds and cell complexes ... Topological manifolds ... Neighborhoods of submanifolds | |
| 650 | 4 | |a Manifolds and cell complexes ... Topological manifolds ... $S {n-1}subset E n$, Schoenflies problem | |
| 650 | 4 | |a Manifolds and cell complexes ... Topological manifolds ... General position and transversality | |
| 650 | 4 | |a Manifolds and cell complexes ... PL-topology ... Triangulating manifolds | |
| 650 | 4 | |a Manifolds and cell complexes ... PL-topology ... Comparison of PL-structures: classification, Hauptvermutung | |
| 650 | 4 | |a Manifolds and cell complexes ... PL-topology ... Regular neighborhoods | |
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Datensatz im Suchindex
| _version_ | 1814789466696450048 |
|---|---|
| adam_text |
Titel: Introduction to 3-manifolds
Autor: Schultens, Jennifer
Jahr: 2014
Contents
Preface ix
Chapter 1. Perspectives on Manifolds 1
§1.1. Topological Manifolds 1
§1.2. Differentiable Manifolds 7
§1.3. Oriented Manifolds 10
§1.4. Triangulated Manifolds 12
§1.5. Geometrie Manifolds 21
§1.6. Connected Sums 23
§1.7. Equivalence of Categories 25
Chapter 2. Surfaces 29
§2.1. A Few Facts about 1-Manifolds 29
§2.2. Classification of Surfaces 31
§2.3. Decompositions of Surfaces 39
§2.4. Covering Spaces and Branched Covering Spaces 41
§2.5. Homotopy and Isotopy on Surfaces 45
§2.6. The Mapping Class Group 47
Chapter 3. 3-Manifolds 55
§3.1. Bundles 56
§3.2. The Schönflies Theorem 62
§3.3. 3-Manifolds that are Prime but Reducible 71
v
vi
Contents
§3.4. Incompressible Surfaces 72
§3.5. Dehn's Lemma* 75
§3.6. Hierarchies* 80
§3.7. Seifert Fibered Spaces 87
§3.8. JSJ Decompositions 96
§3.9. Compendium of Standard Arguments 98
Chapter 4. Knots and Links in 3-Manifolds 101
§4.1. Knots and Links 101
§4.2. Reidemeister Moves 106
§4.3. Basic Constructions 108
§4.4. Knot Invariants 113
§4.5. Zoology 118
§4.6. Braids 122
§4.7. The Alexander Polynomial 126
§4.8. Knots and Height Functions 128
§4.9. The Knot Group* 137
§4.10. Covering Spaces* 139
Chapter 5. Triangulated 3-Manifolds 143
§5.1. Simplicial Complexes 143
§5.2. Normal Surfaces 148
§5.3. Diophantine Systems 155
§5.4. 2-Spheres* 162
§5.5. Prime Decompositions 166
§5.6. Recognition Algorithms 169
§5.7. PL Minimal Surfaces** 172
Chapter 6. Heegaard Splittings 175
§6.1. Handle Decompositions 175
§6.2. Heegaard Diagrams 180
§6.3. Reducibility and Stabilization 182
§6.4. Waldhausen's Theorem 188
§6.5. Structural Theorems 193
§6.6. The Rubinstein-Scharlemann Graphic 196
§6.7. Weak Reducibility and Incompressible Surfaces 200
Contents
vii
§6.8. Generalized Heegaard Splittings 202
§6.9. An Application 208
§6.10. Heegaard Genus and Rank of Fundamental Group* 212
Chapter 7. Further Topics 215
§7.1. Basic Hyperbolic Geometry 215
§7.2. Hyperbolic n-Manifolds** 220
§7.3. Dehn Surgery I 226
§7.4. Dehn Surgery II 232
§7.5. Foliations 238
§7.6. Laminations 243
§7.7. The Curve Complex 248
§7.8. Through the Looking Glass** 252
Appendix A. General Position 261
Appendix B. Morse Functions 269
Bibliography 275
Index 283 |
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| author | Schultens, Jennifer 1965- |
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| isbn | 9781470410209 |
| language | English |
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| spelling | Schultens, Jennifer 1965- Verfasser (DE-588)1054169489 aut Introduction to 3-manifolds Jennifer Schultens Introduction to three-manifolds Providence, RI American Math. Society 2014 X, 286 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 151 Includes bibliographical references and index Manifolds and cell complexes ... Topological manifolds ... Topology of $E 2$, $2$-manifolds msc Manifolds and cell complexes ... Topological manifolds ... Topology of general $3$-manifolds msc Manifolds and cell complexes ... Topological manifolds ... Geometric structures on manifolds msc Manifolds and cell complexes ... Topological manifolds ... Neighborhoods of submanifolds msc Manifolds and cell complexes ... Topological manifolds ... $S {n-1}subset E n$, Schoenflies problem msc Manifolds and cell complexes ... Topological manifolds ... General position and transversality msc Manifolds and cell complexes ... PL-topology ... Triangulating manifolds msc Manifolds and cell complexes ... PL-topology ... Comparison of PL-structures: classification, Hauptvermutung msc Manifolds and cell complexes ... PL-topology ... Regular neighborhoods msc Manifolds and cell complexes ... PL-topology ... Knots and links (in high dimensions) msc Topological manifolds Manifolds (Mathematics) Manifolds and cell complexes ... Topological manifolds ... Topology of $E 2$, $2$-manifolds Manifolds and cell complexes ... Topological manifolds ... Topology of general $3$-manifolds Manifolds and cell complexes ... Topological manifolds ... Geometric structures on manifolds Manifolds and cell complexes ... Topological manifolds ... Neighborhoods of submanifolds Manifolds and cell complexes ... Topological manifolds ... $S {n-1}subset E n$, Schoenflies problem Manifolds and cell complexes ... Topological manifolds ... General position and transversality Manifolds and cell complexes ... PL-topology ... Triangulating manifolds Manifolds and cell complexes ... PL-topology ... Comparison of PL-structures: classification, Hauptvermutung Manifolds and cell complexes ... PL-topology ... Regular neighborhoods Manifolds and cell complexes ... PL-topology ... Knots and links (in high dimensions) Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 s DE-604 Graduate studies in mathematics 151 (DE-604)BV009739289 151 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027331496&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schultens, Jennifer 1965- Introduction to 3-manifolds Graduate studies in mathematics Manifolds and cell complexes ... Topological manifolds ... Topology of $E 2$, $2$-manifolds msc Manifolds and cell complexes ... Topological manifolds ... Topology of general $3$-manifolds msc Manifolds and cell complexes ... Topological manifolds ... Geometric structures on manifolds msc Manifolds and cell complexes ... Topological manifolds ... Neighborhoods of submanifolds msc Manifolds and cell complexes ... Topological manifolds ... $S {n-1}subset E n$, Schoenflies problem msc Manifolds and cell complexes ... Topological manifolds ... General position and transversality msc Manifolds and cell complexes ... PL-topology ... Triangulating manifolds msc Manifolds and cell complexes ... PL-topology ... Comparison of PL-structures: classification, Hauptvermutung msc Manifolds and cell complexes ... PL-topology ... Regular neighborhoods msc Manifolds and cell complexes ... PL-topology ... Knots and links (in high dimensions) msc Topological manifolds Manifolds (Mathematics) Manifolds and cell complexes ... Topological manifolds ... Topology of $E 2$, $2$-manifolds Manifolds and cell complexes ... Topological manifolds ... Topology of general $3$-manifolds Manifolds and cell complexes ... Topological manifolds ... Geometric structures on manifolds Manifolds and cell complexes ... Topological manifolds ... Neighborhoods of submanifolds Manifolds and cell complexes ... Topological manifolds ... $S {n-1}subset E n$, Schoenflies problem Manifolds and cell complexes ... Topological manifolds ... General position and transversality Manifolds and cell complexes ... PL-topology ... Triangulating manifolds Manifolds and cell complexes ... PL-topology ... Comparison of PL-structures: classification, Hauptvermutung Manifolds and cell complexes ... PL-topology ... Regular neighborhoods Manifolds and cell complexes ... PL-topology ... Knots and links (in high dimensions) Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd |
| subject_GND | (DE-588)4185712-4 |
| title | Introduction to 3-manifolds |
| title_alt | Introduction to three-manifolds |
| title_auth | Introduction to 3-manifolds |
| title_exact_search | Introduction to 3-manifolds |
| title_full | Introduction to 3-manifolds Jennifer Schultens |
| title_fullStr | Introduction to 3-manifolds Jennifer Schultens |
| title_full_unstemmed | Introduction to 3-manifolds Jennifer Schultens |
| title_short | Introduction to 3-manifolds |
| title_sort | introduction to 3 manifolds |
| topic | Manifolds and cell complexes ... Topological manifolds ... Topology of $E 2$, $2$-manifolds msc Manifolds and cell complexes ... Topological manifolds ... Topology of general $3$-manifolds msc Manifolds and cell complexes ... Topological manifolds ... Geometric structures on manifolds msc Manifolds and cell complexes ... Topological manifolds ... Neighborhoods of submanifolds msc Manifolds and cell complexes ... Topological manifolds ... $S {n-1}subset E n$, Schoenflies problem msc Manifolds and cell complexes ... Topological manifolds ... General position and transversality msc Manifolds and cell complexes ... PL-topology ... Triangulating manifolds msc Manifolds and cell complexes ... PL-topology ... Comparison of PL-structures: classification, Hauptvermutung msc Manifolds and cell complexes ... PL-topology ... Regular neighborhoods msc Manifolds and cell complexes ... PL-topology ... Knots and links (in high dimensions) msc Topological manifolds Manifolds (Mathematics) Manifolds and cell complexes ... Topological manifolds ... Topology of $E 2$, $2$-manifolds Manifolds and cell complexes ... Topological manifolds ... Topology of general $3$-manifolds Manifolds and cell complexes ... Topological manifolds ... Geometric structures on manifolds Manifolds and cell complexes ... Topological manifolds ... Neighborhoods of submanifolds Manifolds and cell complexes ... Topological manifolds ... $S {n-1}subset E n$, Schoenflies problem Manifolds and cell complexes ... Topological manifolds ... General position and transversality Manifolds and cell complexes ... PL-topology ... Triangulating manifolds Manifolds and cell complexes ... PL-topology ... Comparison of PL-structures: classification, Hauptvermutung Manifolds and cell complexes ... PL-topology ... Regular neighborhoods Manifolds and cell complexes ... PL-topology ... Knots and links (in high dimensions) Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd |
| topic_facet | Manifolds and cell complexes ... Topological manifolds ... Topology of $E 2$, $2$-manifolds Manifolds and cell complexes ... Topological manifolds ... Topology of general $3$-manifolds Manifolds and cell complexes ... Topological manifolds ... Geometric structures on manifolds Manifolds and cell complexes ... Topological manifolds ... Neighborhoods of submanifolds Manifolds and cell complexes ... Topological manifolds ... $S {n-1}subset E n$, Schoenflies problem Manifolds and cell complexes ... Topological manifolds ... General position and transversality Manifolds and cell complexes ... PL-topology ... Triangulating manifolds Manifolds and cell complexes ... PL-topology ... Comparison of PL-structures: classification, Hauptvermutung Manifolds and cell complexes ... PL-topology ... Regular neighborhoods Manifolds and cell complexes ... PL-topology ... Knots and links (in high dimensions) Topological manifolds Manifolds (Mathematics) Topologische Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027331496&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT schultensjennifer introductionto3manifolds AT schultensjennifer introductiontothreemanifolds |