Surface topology:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Woodhead Publ.
2011
|
| Edition: | 3. ed., repr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [241] - 242 |
| Physical Description: | 245 S. zahlr. graph. Darst. |
| ISBN: | 9781898563778 1898563772 |
Staff View
MARC
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| 100 | 1 | |a Firby, Peter A. |d 1946- |e Verfasser |0 (DE-588)1013876288 |4 aut | |
| 245 | 1 | 0 | |a Surface topology |c Peter A. Firby ; Cyril F. Gardiner |
| 250 | |a 3. ed., repr. | ||
| 264 | 1 | |a Oxford [u.a.] |b Woodhead Publ. |c 2011 | |
| 300 | |a 245 S. |b zahlr. graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804148010804838400 |
|---|---|
| adam_text | Table
of
contents
LIST OF SPECIAL SYMBOLS
................................9
AUTHORS PREFACE
.....................................11
PREFACE TO THE THIRD 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
гп
-gons
.................................
53
3.4
Non-orientable
гп^опѕ
...............................57
3.5
The working definition of a surface
.......................59
3.6
The classification theorem
.............................60
Table
of contents
3.7
Summary
........................................61
3.8
Exercises
........................................61
DISTINGUISHING SURFACES
4.1
Introducing
χ(Μ)
...................................64
4.2
χ(Μ)
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
PATTERNS ON SURFACES
5.1
Patterns and
χ(Μ)
..................................77
5.2
Complexes
.......................................82
5.3
Regular complexes
..................................86
5.4
b-
Valent
complexes
.................................90
5.5
Comments
.......................................93
5.6
Exercises
........................................94
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
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
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
11
SURFACES WITH BOUNDARIES
11.1
Definitions and classification theorems
....................205
11.2
Recognising surfaces with boundary
......................212
11.3
An application to knots
.................................216
11.4
Exercise
.............................................219
12
TOPOLOGY, GRAPHS AND GROUPS
222
Outline solutions to the exercises
229
Further reading and references
241
Index
243
|
| any_adam_object | 1 |
| author | Firby, Peter A. 1946- Gardiner, Cyril F. 1930- |
| author_GND | (DE-588)1013876288 (DE-588)109715004 |
| author_facet | Firby, Peter A. 1946- Gardiner, Cyril F. 1930- |
| author_role | aut aut |
| author_sort | Firby, Peter A. 1946- |
| author_variant | p a f pa paf c f g cf cfg |
| building | Verbundindex |
| bvnumber | BV039161734 |
| classification_rvk | SK 280 |
| ctrlnum | (OCoLC)745529988 (DE-599)BVBBV039161734 |
| discipline | Mathematik |
| edition | 3. ed., repr. |
| format | Book |
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| id | DE-604.BV039161734 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:00:20Z |
| institution | BVB |
| isbn | 9781898563778 1898563772 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024179227 |
| oclc_num | 745529988 |
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| owner | DE-29T DE-19 DE-BY-UBM DE-739 DE-83 |
| owner_facet | DE-29T DE-19 DE-BY-UBM DE-739 DE-83 |
| physical | 245 S. zahlr. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Woodhead Publ. |
| record_format | marc |
| spelling | Firby, Peter A. 1946- Verfasser (DE-588)1013876288 aut Surface topology Peter A. Firby ; Cyril F. Gardiner 3. ed., repr. Oxford [u.a.] Woodhead Publ. 2011 245 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. [241] - 242 Topologie (DE-588)4060425-1 gnd rswk-swf Geometrische Topologie (DE-588)4156724-9 gnd rswk-swf Fläche (DE-588)4129864-0 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 Kompakte Fläche (DE-588)4412571-9 s Topologie (DE-588)4060425-1 s DE-604 Geometrische Topologie (DE-588)4156724-9 s Flächentheorie (DE-588)4475211-8 s 1\p DE-604 Oberfläche (DE-588)4042907-6 s 2\p DE-604 Fläche (DE-588)4129864-0 s 3\p DE-604 Gardiner, Cyril F. 1930- Verfasser (DE-588)109715004 aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024179227&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 |
| spellingShingle | Firby, Peter A. 1946- Gardiner, Cyril F. 1930- Surface topology Topologie (DE-588)4060425-1 gnd Geometrische Topologie (DE-588)4156724-9 gnd Fläche (DE-588)4129864-0 gnd Oberfläche (DE-588)4042907-6 gnd Flächentheorie (DE-588)4475211-8 gnd Kompakte Fläche (DE-588)4412571-9 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4156724-9 (DE-588)4129864-0 (DE-588)4042907-6 (DE-588)4475211-8 (DE-588)4412571-9 |
| title | Surface topology |
| title_auth | Surface topology |
| title_exact_search | Surface topology |
| title_full | Surface topology Peter A. Firby ; Cyril F. Gardiner |
| title_fullStr | Surface topology Peter A. Firby ; Cyril F. Gardiner |
| title_full_unstemmed | Surface topology Peter A. Firby ; Cyril F. Gardiner |
| title_short | Surface topology |
| title_sort | surface topology |
| topic | Topologie (DE-588)4060425-1 gnd Geometrische Topologie (DE-588)4156724-9 gnd Fläche (DE-588)4129864-0 gnd Oberfläche (DE-588)4042907-6 gnd Flächentheorie (DE-588)4475211-8 gnd Kompakte Fläche (DE-588)4412571-9 gnd |
| topic_facet | Topologie Geometrische Topologie Fläche Oberfläche Flächentheorie Kompakte Fläche |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024179227&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT firbypetera surfacetopology AT gardinercyrilf surfacetopology |