Graphs, surfaces and homology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 251 S. Ill., graph. Darst. |
| ISBN: | 9780521154055 9780521766654 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804143587342942208 |
|---|---|
| adam_text | Titel: Graphs, surfaces, and homology
Autor: Giblin, Peter
Jahr: 2010
Contents
Preface to the third edition page xi
Preface to the first edition xiii
List of notation xvii
Introduction 1
1 Graphs 9
Abstract graphs and realizations 9
Kirchhoff s laws 14
Maximal trees and the cyclomatic number 16
Chains and cycles on an oriented graph 20
Planar graphs 26
Appendix on Kirchhoff s equations 35
2 Closed surfaces 38
Closed surfaces and orientability 39
Polygonal representation of a closed surface 45
A note on realizations 47
Transformation of closed surfaces to standard form 49
Euler characteristics 55
Minimal triangulations 60
3 Simplicial complexes 67
Simplexes 67
Ordered simplexes and oriented simplexes 73
Simplicial complexes 74
Abstract simplicial complexes and realizations 77
Triangulations and diagrams of simplicial complexes 79
Stars, joins and links 84
vii
viii Contents
Collapsing 88
Appendix on orientation 93
4 Homology groups 99
Chain groups and boundary homomorphisms 99
Homology groups 104
Relative homology groups 112
Three homomorphisms 121
Appendix on chain complexes 124
5 The question of invariance 127
In variance under stellar subdivision 128
Triangulations, simplicial approximation and topological
invariance 133
Appendix on barycentric subdivision 136
6 Some general theorems 138
The homology sequence of a pair 138
The excision theorem 142
Collapsing revisited 144
Homology groups of closed surfaces 149
The Euler characteristic 154
7 Two more general theorems 158
The Mayer-Vietoris sequence 158
Homology sequence of a triple 167
8 Homology modulo 2 171
9 Graphs in surfaces 180
Regular neighbourhoods 183
Surfaces 187
Lefschetz duality 191
A three-dimensional situation 195
Separating surfaces by graphs 198
Representation of homology elements by simple closed polygons 200
Orientation preserving and reversing loops 203
A generalization of Euler s formula 207
Brussels Sprouts 211
Appendix: abelian groups 215
Basic definitions 215
Finitely generated (f.g.) and free abelian groups 217
Contents ix
Quotient groups 219
Exact sequences 221
Direct sums and splitting 222
Presentations 226
Rank of a f.g. abelian group 233
References 239
Index 243
|
| any_adam_object | 1 |
| author | Giblin, Peter 1943- |
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| dewey-full | 514/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.2 |
| dewey-search | 514/.2 |
| dewey-sort | 3514 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:50:02Z |
| institution | BVB |
| isbn | 9780521154055 9780521766654 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020794840 |
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| physical | XX, 251 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
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| publisher | Cambridge Univ. Press |
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| spelling | Giblin, Peter 1943- Verfasser (DE-588)13875750X aut Graphs, surfaces and homology Peter Giblin 3. ed. Cambridge [u.a.] Cambridge Univ. Press 2010 XX, 251 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Homologietheorie (DE-588)4141714-8 gnd rswk-swf Abelsche Gruppe (DE-588)4140988-7 gnd rswk-swf Homologietheorie (DE-588)4141714-8 s DE-604 Algebraische Topologie (DE-588)4120861-4 s Abelsche Gruppe (DE-588)4140988-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020794840&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Giblin, Peter 1943- Graphs, surfaces and homology Algebraische Topologie (DE-588)4120861-4 gnd Homologietheorie (DE-588)4141714-8 gnd Abelsche Gruppe (DE-588)4140988-7 gnd |
| subject_GND | (DE-588)4120861-4 (DE-588)4141714-8 (DE-588)4140988-7 |
| title | Graphs, surfaces and homology |
| title_auth | Graphs, surfaces and homology |
| title_exact_search | Graphs, surfaces and homology |
| title_full | Graphs, surfaces and homology Peter Giblin |
| title_fullStr | Graphs, surfaces and homology Peter Giblin |
| title_full_unstemmed | Graphs, surfaces and homology Peter Giblin |
| title_short | Graphs, surfaces and homology |
| title_sort | graphs surfaces and homology |
| topic | Algebraische Topologie (DE-588)4120861-4 gnd Homologietheorie (DE-588)4141714-8 gnd Abelsche Gruppe (DE-588)4140988-7 gnd |
| topic_facet | Algebraische Topologie Homologietheorie Abelsche Gruppe |
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