Surface topology:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Horwood
1991
|
| Edition: | 2. ed. |
| Series: | Mathematics and its applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 220 S. Ill., graph. Darst. |
| ISBN: | 0138553211 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804135860742914048 |
|---|---|
| adam_text | Table of contents
LIST OF SPECIAL SYMBOLS 9
AUTHORS PREFACE 11
PREFACE TO THE SECOND EDITION 13
1 INTUITIVE IDEAS
1.1 Introduction 15
1.2 Preliminary skirmish 16
1.3 Models 18
1.4 Connected sets 19
1.5 Problem surfaces 20
1.6 Homeomorphic surfaces 21
1.7 Some basic surfaces 24
1.8 Orientability 27
1.9 The connected sum construction 28
1.10 Summary 29
1.11 Exercises 29
2 PLANE MODELS OF SURFACES
2.1 The basic plane models 32
2.2 Paper models of the basic surfaces 37
2.3 Plane models and orientability 38
2.4 Connected sums of the basic surfaces 38
2.5 Summary 38
2.6 Comments 39
2.7 Exercises 42
3 SURFACES AS PLANE DIAGRAMS
3.1 Plane models and the connected sum construction 49
3.2 Algebraic description of surfaces 51
3.3 Orientable 2n gons 53
3.4 Non orientable 2n gons 57
3.5 The working definition of a surface 59
3.6 The classification theorem 60
6 Table of contents
3.7 Summary 61
3.8 Exercises 61
4 DISTINGUISHING SURFACES
4.1 Introducing %{M) 64
4.2 x{M) and the connected sum construction 65
4.3 How to tell the difference 68
4.4 Can you tell the difference? 69
4.5 Comments 70
4.6 Exercises 71
5 PATTERNS ON SURFACES
5.1 Patterns and %(M) 77
5.2 Complexes 82
5.3 Regular complexes 86
5.4 b Valent complexes 90
5.5 Comments 93
5.6 Exercises 94
6 MAPS AND GRAPHS
6.1 Colouring maps on surfaces 101
6.2 Embedding graphs in surfaces 105
6.3 Planar graphs 108
6.4 Outerplanar graphs 109
6.5 Embedding the complete graphs 109
6.6 Sprouts 112
6.7 Brussels sprouts 114
6.8 Comments 114
6.9 Exercises 116
7 VECTOR FIELDS ON SURFACES
7.1 A water proof 120
7.2 Hairy surfaces 122
7.3 Interpretations of the index theorem 129
7.4 Lakes 130
7.5 Islands in lakes 131
7.6 Islands 134
7.7 Vector fields and differential equations 134
7.8 Comments 137
7.9 Exercises 138
8 PLANE TESSELLATION REPRESENTATIONS OF COMPACT
SURFACES
8.1 Plane Euclidean geometry 141
8.2 Groups 144
Table of contents 7
8.3 Plane hyperbolic geometry 150
8.4 Plane tessellations 154
8.5 Comments 175
8.6 Exercises 176
9 SOME APPLICATIONS OF TESSELLATION REPRESENTATIONS
9.1 Introduction 181
9.2 Tessellations and patterns 181
9.3 Tessellations and map colouring 185
9.4 Tessellations and vector fields 187
9.5 Summary 196
9.6 Exercises 196
10 INTRODUCING THE FUNDAMENTAL GROUP
10.1 Introduction 199
10.2 The fundamental group 200
10.3 Isomorphic groups 201
10.4 Comments 202
10.5 Exercises 203
Outline solutions to the exercises 205
Further reading and references 216
Index 218
|
| adam_txt |
Table of contents
LIST OF SPECIAL SYMBOLS 9
AUTHORS' PREFACE 11
PREFACE TO THE SECOND EDITION 13
1 INTUITIVE IDEAS
1.1 Introduction 15
1.2 Preliminary skirmish 16
1.3 Models 18
1.4 Connected sets 19
1.5 Problem surfaces 20
1.6 Homeomorphic surfaces 21
1.7 Some basic surfaces 24
1.8 Orientability 27
1.9 The connected sum construction 28
1.10 Summary 29
1.11 Exercises 29
2 PLANE MODELS OF SURFACES
2.1 The basic plane models 32
2.2 Paper models of the basic surfaces 37
2.3 Plane models and orientability 38
2.4 Connected sums of the basic surfaces 38
2.5 Summary 38
2.6 Comments 39
2.7 Exercises 42
3 SURFACES AS PLANE DIAGRAMS
3.1 Plane models and the connected sum construction 49
3.2 Algebraic description of surfaces 51
3.3 Orientable 2n gons 53
3.4 Non orientable 2n gons 57
3.5 The working definition of a surface 59
3.6 The classification theorem 60
6 Table of contents
3.7 Summary 61
3.8 Exercises 61
4 DISTINGUISHING SURFACES
4.1 Introducing %{M) 64
4.2 x{M) and the connected sum construction 65
4.3 How to tell the difference 68
4.4 Can you tell the difference? 69
4.5 Comments 70
4.6 Exercises 71
5 PATTERNS ON SURFACES
5.1 Patterns and %(M) 77
5.2 Complexes 82
5.3 Regular complexes 86
5.4 b Valent complexes 90
5.5 Comments 93
5.6 Exercises 94
6 MAPS AND GRAPHS
6.1 Colouring maps on surfaces 101
6.2 Embedding graphs in surfaces 105
6.3 Planar graphs 108
6.4 Outerplanar graphs 109
6.5 Embedding the complete graphs 109
6.6 Sprouts 112
6.7 Brussels sprouts 114
6.8 Comments 114
6.9 Exercises 116
7 VECTOR FIELDS ON SURFACES
7.1 A water proof 120
7.2 Hairy surfaces 122
7.3 Interpretations of the index theorem 129
7.4 Lakes 130
7.5 Islands in lakes 131
7.6 Islands 134
7.7 Vector fields and differential equations 134
7.8 Comments 137
7.9 Exercises 138
8 PLANE TESSELLATION REPRESENTATIONS OF COMPACT
SURFACES
8.1 Plane Euclidean geometry 141
8.2 Groups 144
Table of contents 7
8.3 Plane hyperbolic geometry 150
8.4 Plane tessellations 154
8.5 Comments 175
8.6 Exercises 176
9 SOME APPLICATIONS OF TESSELLATION REPRESENTATIONS
9.1 Introduction 181
9.2 Tessellations and patterns 181
9.3 Tessellations and map colouring 185
9.4 Tessellations and vector fields 187
9.5 Summary 196
9.6 Exercises 196
10 INTRODUCING THE FUNDAMENTAL GROUP
10.1 Introduction 199
10.2 The fundamental group 200
10.3 Isomorphic groups 201
10.4 Comments 202
10.5 Exercises 203
Outline solutions to the exercises 205
Further reading and references 216
Index 218 |
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| author | Firby, Peter A. Gardiner, Cyril F. 1930- |
| author_GND | (DE-588)109715004 |
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| author_sort | Firby, Peter A. |
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| building | Verbundindex |
| bvnumber | BV021910928 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA612 |
| callnumber-search | QA612 |
| callnumber-sort | QA 3612 |
| callnumber-subject | QA - Mathematics |
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| dewey-ones | 514 - Topology |
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| dewey-sort | 3514 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV021910928 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:05:15Z |
| indexdate | 2024-07-09T20:47:13Z |
| institution | BVB |
| isbn | 0138553211 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015126102 |
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| owner_facet | DE-706 |
| physical | 220 S. Ill., graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Horwood |
| record_format | marc |
| series2 | Mathematics and its applications |
| spelling | Firby, Peter A. Verfasser aut Surface topology P. A. Firby ; C. F. Gardiner 2. ed. New York [u.a.] Horwood 1991 220 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications Algebraic topology Surfaces Topologie (DE-588)4060425-1 gnd rswk-swf Oberfläche (DE-588)4042907-6 gnd rswk-swf Flächentheorie (DE-588)4475211-8 gnd rswk-swf Kompakte Fläche (DE-588)4412571-9 gnd rswk-swf Fläche (DE-588)4129864-0 gnd rswk-swf Geometrische Topologie (DE-588)4156724-9 gnd rswk-swf Fläche (DE-588)4129864-0 s DE-604 Topologie (DE-588)4060425-1 s Flächentheorie (DE-588)4475211-8 s 1\p DE-604 Oberfläche (DE-588)4042907-6 s 2\p DE-604 Kompakte Fläche (DE-588)4412571-9 s 3\p DE-604 Geometrische Topologie (DE-588)4156724-9 s 4\p DE-604 Gardiner, Cyril F. 1930- Verfasser (DE-588)109715004 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015126102&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Firby, Peter A. Gardiner, Cyril F. 1930- Surface topology Algebraic topology Surfaces Topologie (DE-588)4060425-1 gnd Oberfläche (DE-588)4042907-6 gnd Flächentheorie (DE-588)4475211-8 gnd Kompakte Fläche (DE-588)4412571-9 gnd Fläche (DE-588)4129864-0 gnd Geometrische Topologie (DE-588)4156724-9 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4042907-6 (DE-588)4475211-8 (DE-588)4412571-9 (DE-588)4129864-0 (DE-588)4156724-9 |
| title | Surface topology |
| title_auth | Surface topology |
| title_exact_search | Surface topology |
| title_exact_search_txtP | Surface topology |
| title_full | Surface topology P. A. Firby ; C. F. Gardiner |
| title_fullStr | Surface topology P. A. Firby ; C. F. Gardiner |
| title_full_unstemmed | Surface topology P. A. Firby ; C. F. Gardiner |
| title_short | Surface topology |
| title_sort | surface topology |
| topic | Algebraic topology Surfaces Topologie (DE-588)4060425-1 gnd Oberfläche (DE-588)4042907-6 gnd Flächentheorie (DE-588)4475211-8 gnd Kompakte Fläche (DE-588)4412571-9 gnd Fläche (DE-588)4129864-0 gnd Geometrische Topologie (DE-588)4156724-9 gnd |
| topic_facet | Algebraic topology Surfaces Topologie Oberfläche Flächentheorie Kompakte Fläche Fläche Geometrische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015126102&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT firbypetera surfacetopology AT gardinercyrilf surfacetopology |