Algorithmic and computer methods for three-manifolds:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1997
|
| Series: | Mathematics and its applications
425 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Frühere Ausg. u.d.T.: Matveev, Sergej V.: Algorithmical and computer methods in three-dimensional topology |
| Physical Description: | XII, 334 S. Ill., graph. Darst. |
| ISBN: | 0792347706 |
Staff View
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| 245 | 1 | 0 | |a Algorithmic and computer methods for three-manifolds |c by A. T. Fomenko and S. V. Matveev |
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Record in the Search Index
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|---|---|
| adam_text |
TABLE OF CONTENTS
Series editor's preface v
Preface xi
Chapter 1. Preliminary information
1.1 On the style of presentation 1
1.2 Some facts from general topology 1
1.3 Gluings 4
1.4 Polyhedra and complexes 5
1.5 Fundamental groups 9
1.6 An algorithm for the calculation of the fundamental group 10
1.7 The second homotopy group and the first homology group 15
1.8 Manifolds 15
1.9 Fibrations and coverings 22
1.10 General position and transversality 23
1.11 Handles 27
1.12 Algorithmic problems 30
1.13 Sources of additional information 31
Chapter 2. Surfaces
2.1 Examples of surfaces 33
2.2 Classification of surfaces 35
2.3 Homotopy equivalence of surfaces 41
2.4 Cutting gluing surgery 49
2.5 Applications of cutting gluing surgery 60
2.6 The Dehn lemma and the loop theorem 64
2.7 Algorithmic problems 69
Chapter 3. The homeotopy group of a surface
3.1 The homeotopy group 71
3.2 Twists 71
3.3 The homeotopy group of a disc modulo boundary 73
3.4 The braid group 73
3.5 The pure braid group 77
3.6 The homeotopy groups of a disc with holes 79
3.7 The homeotopy group of an arbitrary surface is generated by twists 81
3.8 Finite generation of the homeotopy group of an arbitrary surface by twists 86
3.9 The homeotopy group of a handlebody 93
3.10 Comments 107
viii Computer Topology and 3 Manifolds
Chapter 4. The presentation of three dimensional manifolds by the
identification of faces of polyhedra
4.1 Three dimensional manifolds with conic singularities 109
4.2 The criterion of the absence of singularities 112
4.3 Lens spaces 114
4.4 Manifolds of genus 1 120
Chapter 5. Heegaard splittings and Heegaard Diagrams
5.1 The Heegaard splitting 123
5.2 Stable equivalence of Heegaard splittings 125
5.3 Heegaard diagrams 129
5.4 Equivalent diagrams 130
5.5 Normalized diagrams 132
5.6 Wave transformation of the Heegaard diagram 135
5.7 The structure of Heegaard diagrams of genus 2 137
5.8 On the enumeration of three dimensional manifolds 142
Chapter 6. Algorithmic recognition of the sphere
6.1 On the formulation of the classification problem
for three dimensional manifolds 145
6.2 The algorithm for recognition of a sphere S3 in the class
of manifolds of genus 2 146
6.3 Comments to chapters 5.6 157
Chapter 7. Connected sums
7.1 The properties of connected summation 159
7.2 Irreducible and prime manifolds 160
7.3 The theory of normal surfaces 165
7.4 The existence of decomposition into prime summands 171
7.5 Uniqueness of decomposition into prime summands 174
Chapter 8. Knots and links
8.1 Basic Definitions 179
8.2 Distributive groupoids in the knot theory 182
8.3 The Conway approach 192
8.4 Special realizations of the invariant w 202
8.5 The linking coefficient 205
Chapter 9. Surgery Along Links
9.1 Integral surgery and three dimensional manifolds 207
9.2 Surgery along framed links and cobordism 209
Contents ix
9.3 The Kirby calculus 211
9.4 Even surgery 215
9.5 Presentations of homology spheres 221
9.6 On Heegaard diagrams of homology spheres 226
9.7 Sources and comments 228
Chapter 10. Seifert Manifolds
10.1 The definition of a Seifert manifold 229
10.2 The base of a Seifert manifold 232
10.3 Seifert manifolds without singular fibers 233
10.4 Seifert manifolds with singular fibers 237
10.5 The Euler number and the fiberwise classification of Seifert manifolds 238
10.6 The fundamental group of a Seifert manifold 241
10.7 Seifert manifolds with boundary 244
10.8 Incompressibility of the boundary 244
10.9 Irreducibility of Seifert manifolds with boundary 245
10.10 Fiberwise character of annuli with fiberwise boundaries 245
10.11 Fiberwise nature of essential annuli 247
10.12 Large Seifert manifolds 255
10.13 Fiberwise nature of incompressible tori 256
10.14 Topological classification of large closed Seifert manifolds 258
10.15 Small Seifert manifolds with finite fundamental groups 259
10.16 Small Seifert manifolds with infinite fundamental groups 267
Chapter 11. Class 3i
11.1 Definition and the simplest properties of class M 271
11.2 Rough and thin tori 274
11.3 Classification of class .# manifolds 276
11.4 Class 3i and iterated torus links 283
Chapter 12. The Haken Method
12.1 Normal surfaces as solutions of a system of equations 287
12.2 Fundamental sets of solutions 290
12.3 Geometric summation 291
12.4 The Haken algorithm 294
12. 5 An example of stability 295
12.6 An algorithm for the recognition of the trivial knot 297
Comments on the Figures 299
References 323
Index 327 |
| any_adam_object | 1 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV011798696 |
| illustrated | Illustrated |
| indexdate | 2024-11-05T17:03:41Z |
| institution | BVB |
| isbn | 0792347706 |
| language | English |
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| physical | XII, 334 S. Ill., graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Fomenko, Anatolij Timofeevič 1945- Verfasser (DE-588)119092689 aut Algorithmic and computer methods for three-manifolds by A. T. Fomenko and S. V. Matveev Dordrecht [u.a.] Kluwer 1997 XII, 334 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 425 Frühere Ausg. u.d.T.: Matveev, Sergej V.: Algorithmical and computer methods in three-dimensional topology Three-manifolds (Topology) Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Dimension 3 (DE-588)4321722-9 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s Algorithmus (DE-588)4001183-5 s DE-604 Matveev, Sergej V. 1947- Verfasser (DE-588)124843956 aut Mathematics and its applications 425 (DE-604)BV008163334 425 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007965708&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fomenko, Anatolij Timofeevič 1945- Matveev, Sergej V. 1947- Algorithmic and computer methods for three-manifolds Mathematics and its applications Three-manifolds (Topology) Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 3 (DE-588)4321722-9 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4321722-9 (DE-588)4001183-5 |
| title | Algorithmic and computer methods for three-manifolds |
| title_auth | Algorithmic and computer methods for three-manifolds |
| title_exact_search | Algorithmic and computer methods for three-manifolds |
| title_full | Algorithmic and computer methods for three-manifolds by A. T. Fomenko and S. V. Matveev |
| title_fullStr | Algorithmic and computer methods for three-manifolds by A. T. Fomenko and S. V. Matveev |
| title_full_unstemmed | Algorithmic and computer methods for three-manifolds by A. T. Fomenko and S. V. Matveev |
| title_short | Algorithmic and computer methods for three-manifolds |
| title_sort | algorithmic and computer methods for three manifolds |
| topic | Three-manifolds (Topology) Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 3 (DE-588)4321722-9 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Three-manifolds (Topology) Mannigfaltigkeit Dimension 3 Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007965708&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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