A guide to the classification theorem for compact surfaces:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
|
| Series: | Geometry and Computing
9 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 178 S. Ill., graph. Darst. 235 mm x 155 mm |
| ISBN: | 3642343635 9783642343636 |
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MARC
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| 245 | 1 | 0 | |a A guide to the classification theorem for compact surfaces |c Jean Gallier ; Dianna Xu |
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Record in the Search Index
| _version_ | 1807955073977810944 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 THE CLASSIFICATION THEOREM: INFORMAL PRESENTATION 1
1.1 INTRODUCTION 1
1.2 INFORMAL PRESENTATION OF THE THEOREM 4
REFERENCES 20
2 SURFACES 21
2.1 THE QUOTIENT TOPOLOGY 21
2.2 SURFACES: A FORMAL DEFINITION 23
REFERENCES 25
3 SIMPLICES, COMPLEXES, AND TRIANGULATIONS 27
3.1 SIMPLICES AND COMPLEXES 27
3.2 TRIANGULATIONS 32
REFERENCES 35
4 THE FUNDAMENTAL GROUP, ORIENTABILITY 37
4.1 THE FUNDAMENTAL GROUP 37
4.2 THE WINDING NUMBER OF A CLOSED PLANE CURVE 42
4.3 THE FUNDAMENTAL GROUP OF THE PUNCTURED PLANE 45
4.4 THE DEGREE OF A MAP IN THE PLANE 46
4.5 ORIENTABILITY OF A SURFACE 47
4.6 SURFACES WITH BOUNDARY 48
REFERENCES 51
5 HOMOLOGY GROUPS 53
5.1 FINITELY GENERATED ABELIAN GROUPS 53
5.2 SIMPLICIAL AND SINGULAR HOMOLOGY 57
5.3 HOMOLOGY GROUPS OF THE FINITE POLYHEDRA 73
REFERENCES 77
6 THE CLASSIFICATION THEOREM FOR COMPACT SURFACES 79
6.1 CELL COMPLEXES 79
6.2 NORMAL FORM FOR CELL COMPLEXES 83
X I
HTTP://D-NB.INFO/102618469X
IMAGE 2
XII CONTENTS
6.3 PROOF OF THE CLASSIFICATION THEOREM 94
6.4 CONNECTED SUMS AND THE CLASSIFICATION THEOREM 95
6.5 OTHER COMBINATORIAL PROOFS 97
6.6 APPLICATION OF THE MAIN THEOREM: DETERMINING THE FUNDAMENTAL GROUPS
OF COMPACT SURFACES 99
REFERENCES 102
A VIEWING THE REAL PROJECTIVE PLANE IN R 3 ; THE CROSS-CAP AND THE
STEINER ROMAN SURFACE 1 05
REFERENCES 112
B PROOF OF PROPOSITION 5.1 113
C TOPOLOGICAL PRELIMINARIES 117
C. 1 METRIC SPACES AND NORMED VECTOR SPACES 117
C.2 TOPOLOGICAL SPACES, CONTINUOUS FUNCTIONS, LIMITS 121
C.3 CONNECTED SETS 129
C.4 COMPACT SETS 136
REFERENCES 149
D HISTORY OF THE CLASSIFICATION THEOREM 151
REFERENCES 157
E EVERY SURFACE CAN BE TRIANGULATED 159
REFERENCES 165
F NOTES 167
REFERENCES 172
SYMBOL INDEX 173
INDEX 175 |
| any_adam_object | 1 |
| author | Gallier, Jean H. 1949- Xu, Dianna |
| author_GND | (DE-588)122585615 (DE-588)1031896104 |
| author_facet | Gallier, Jean H. 1949- Xu, Dianna |
| author_role | aut aut |
| author_sort | Gallier, Jean H. 1949- |
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| bvnumber | BV040740869 |
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| ctrlnum | (OCoLC)835294805 (DE-599)DNB102618469X |
| 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 | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-08-21T00:31:58Z |
| institution | BVB |
| isbn | 3642343635 9783642343636 |
| language | English |
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| physical | XII, 178 S. Ill., graph. Darst. 235 mm x 155 mm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series | Geometry and Computing |
| series2 | Geometry and Computing |
| spelling | Gallier, Jean H. 1949- Verfasser (DE-588)122585615 aut A guide to the classification theorem for compact surfaces Jean Gallier ; Dianna Xu Berlin [u.a.] Springer 2013 XII, 178 S. Ill., graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Geometry and Computing 9 Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Kompakte Fläche (DE-588)4412571-9 gnd rswk-swf Kompakte Fläche (DE-588)4412571-9 s Algebraische Topologie (DE-588)4120861-4 s DE-604 Xu, Dianna Verfasser (DE-588)1031896104 aut Erscheint auch als Online-Ausgabe 978-3-642-34364-3 Geometry and Computing 9 (DE-604)BV022959018 9 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4126806&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025720814&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gallier, Jean H. 1949- Xu, Dianna A guide to the classification theorem for compact surfaces Geometry and Computing Algebraische Topologie (DE-588)4120861-4 gnd Kompakte Fläche (DE-588)4412571-9 gnd |
| subject_GND | (DE-588)4120861-4 (DE-588)4412571-9 |
| title | A guide to the classification theorem for compact surfaces |
| title_auth | A guide to the classification theorem for compact surfaces |
| title_exact_search | A guide to the classification theorem for compact surfaces |
| title_full | A guide to the classification theorem for compact surfaces Jean Gallier ; Dianna Xu |
| title_fullStr | A guide to the classification theorem for compact surfaces Jean Gallier ; Dianna Xu |
| title_full_unstemmed | A guide to the classification theorem for compact surfaces Jean Gallier ; Dianna Xu |
| title_short | A guide to the classification theorem for compact surfaces |
| title_sort | a guide to the classification theorem for compact surfaces |
| topic | Algebraische Topologie (DE-588)4120861-4 gnd Kompakte Fläche (DE-588)4412571-9 gnd |
| topic_facet | Algebraische Topologie Kompakte Fläche |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4126806&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025720814&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022959018 |
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