The classification of knots and 3-dimensional spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford u.a.
Oxford Univ. Press
1992
|
| Schriftenreihe: | Oxford science publications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 162 S. Ill. |
| ISBN: | 0198596979 |
Internformat
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| 100 | 1 | |a Hemion, Geoffrey |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The classification of knots and 3-dimensional spaces |c Geoffrey Hemion |
| 264 | 1 | |a Oxford u.a. |b Oxford Univ. Press |c 1992 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
1 Introduction 3
PART I PRELIMINARIES
2 What is a knot? 9
3 How to compare two knots 14
4 The theory of compact surfaces 19
5 Piecewise linear topology 30
PART II THE THEORY OF NORMAL SURFACES
6 Incompressible surfaces 41
7 Normal surfaces 47
8 Diophantine inequalities 53
9 Fundamental solutions 56
10 The easy case 64
11 The difficult case 69
12 Why is the difficult case difficult? 74
13 What to do in the difficult case 78
PART III CLASSIFYING HOMEOMORPHISMS OF SURFACES
14 Straightening homeomorphisms 87
15 The conjugacy problem 92
16 The hyperbolic plane 95
17 Movements of the hyperbolic plane 102
18 The size of a homeomorphism 106
19 Small curves 110
20 Small conjugating homeomorphisms 112
21 Classifying mappings of surfaces 117
22 The final result 119
2 Contents
A Homeomorphisms of surfaces 123
A.I Isotopies of/, g, and h 125
A.1.1 Some preliminary results and definitions 125
A. 1.2 The definition of the fundamental region 127
A.1.3 The size of a homeomorphism 128
A.1.4 New choices for /, g, and h 129
A. 1.5 The elimination of trivial intersections 130
A. 1.6 Straightening the homeomorphisms 131
A.1.7 Agreement between / • h and h ¦ g on xQ 133
A. 1.8 Agreement between fh and h g everywhere 135
A.2 The small curve, c 138
A.2.1 The definition of the arcs 7n 138
A.2.2 The basic idea for constructing c 139
A.2.3 The link of B and the definition of a par¬
ticular case 141
A.2.4 The points zt 142
A.2.5 Non parallelity regions in the fundamental
regions 143
A.2.6 Constructing the curve c in our special case 145
A.2.7 Proving that c is not deformable to a bound¬
ary in our special case 147
A.2.8 The second special case: many 7* pass through
a 149
A.2.9 The third, and last, special case: all 7* pass
through a 152
A.3 Solution of conjugacy problem 154
A.3.1 Estimating the size of h 154
A.3.2 The generalization to surfaces without bound¬
ary 156
A.3.3 The proof of the conjugacy theorem 158
List of figures 160
Index 163
|
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| discipline | Mathematik |
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| id | DE-604.BV008019906 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:13:00Z |
| institution | BVB |
| isbn | 0198596979 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005276695 |
| oclc_num | 246836303 |
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| physical | 162 S. Ill. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Oxford science publications |
| spelling | Hemion, Geoffrey Verfasser aut The classification of knots and 3-dimensional spaces Geoffrey Hemion Oxford u.a. Oxford Univ. Press 1992 162 S. Ill. txt rdacontent n rdamedia nc rdacarrier Oxford science publications Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Dimension 3 (DE-588)4321722-9 gnd rswk-swf Knotentheorie (DE-588)4164318-5 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s Knotentheorie (DE-588)4164318-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005276695&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hemion, Geoffrey The classification of knots and 3-dimensional spaces Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 3 (DE-588)4321722-9 gnd Knotentheorie (DE-588)4164318-5 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4321722-9 (DE-588)4164318-5 |
| title | The classification of knots and 3-dimensional spaces |
| title_auth | The classification of knots and 3-dimensional spaces |
| title_exact_search | The classification of knots and 3-dimensional spaces |
| title_full | The classification of knots and 3-dimensional spaces Geoffrey Hemion |
| title_fullStr | The classification of knots and 3-dimensional spaces Geoffrey Hemion |
| title_full_unstemmed | The classification of knots and 3-dimensional spaces Geoffrey Hemion |
| title_short | The classification of knots and 3-dimensional spaces |
| title_sort | the classification of knots and 3 dimensional spaces |
| topic | Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 3 (DE-588)4321722-9 gnd Knotentheorie (DE-588)4164318-5 gnd |
| topic_facet | Mannigfaltigkeit Dimension 3 Knotentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005276695&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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