Algebraic topology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
London
Van Nostrand Reinhold Comp.
1972
|
| Ausgabe: | Repr. |
| Schriftenreihe: | The new university mathematics series.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX,375 S. |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804117239219093504 |
|---|---|
| adam_text | CONTENTS
Introduction
Chapter 1 Algebraic and Topological Preliminaries
1.1 Introduction 1
1.2 Set theory 1
1.3 Algebra 3
1.4 Analytic topology 15
Chapter 2 Homotopy and Simplicial Complexes
2.1 Introduction 23
2.2 The classification problem; homotopy 23
2.3 Simplicial complexes 31
2.4 Homotopy and homeomorphism of polyhedra 40
2.5 Subdivision and the Simplicial Approximation Theorem 45
Exercises 59
Notes on Chapter 2 61
Chapter 3 The Fundamental Group
3.1 Introduction 63
3.2 Definition and elementary properties of the fundamental
group 63
3.3 Methods of calculation 71
3.4 Classification of triangulable 2-manifolds 87
Exercises 99
Notes on Chapter 3 103
Chapter 4 Homology Theory
4.1 Introduction 104
4.2 Homology groups 104
4.3 Methods of calculation: simplicial homology 113
4.4 Methods of calculation: exact sequences 124
vii
viii CONTENTS
4.5 Homology groups with arbitrary coefficients, and the
Lefschetz Fixed-Point Theorem 141
Exercises 151
Notes on Chapter 4 156
Chapter 5 Cohomology and Duality Theorems
5.1 Introduction 158
5.2 Definitions and calculation theorems 159
5.3 The Alexander-Poincare Duality Theorem 170
5.4 Manifolds with boundary and the Lefschetz Duality
Theorem 184
Exercises 195
Notes on Chapter 5 198
Chapter 6 General Homotopy Theory
6.1 Introduction 200
6.2 Some geometric constructions 201
6.3 Homotopy classes of maps 222
6.4 Exact sequences 233
6.5 Fibre and cofibre maps 243
Exercises 250
Notes on Chapter 6 254
Chapter 7 Homotopy Groups and CW-Complexes
7.1 Introduction 257
7.2 Homotopy groups 258
7.3 CW-complexes 273
7.4 Homotopy groups of CW-complexes 287
7.5 The theorem of J. H. C. Whitehead and the Cellular
Approximation Theorem 298
Exercises 304
Notes on Chapter 7 309
Chapter 8
Homology and Cohomology of CW-Complexes
8.1 Introduction 311
8.2 The Excision Theorem and cellular homology 311
8.3 The Hurewicz theorem 322
CONTENTS IX
8.4 Cohomology and Eilenberg-MacLane spaces 330
8.5 Products 339
Exercises 352
Notes on Chapter 8 359
References 361
Index 369
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| any_adam_object | 1 |
| author | Maunder, Charles R. F. 1937-2018 |
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| discipline | Mathematik |
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| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:51:14Z |
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| publishDate | 1972 |
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| series2 | The new university mathematics series. |
| spelling | Maunder, Charles R. F. 1937-2018 Verfasser (DE-588)129582484 aut Algebraic topology C. R. F. Maunder* Repr. London Van Nostrand Reinhold Comp. 1972 IX,375 S. txt rdacontent n rdamedia nc rdacarrier The new university mathematics series. Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001845217&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Maunder, Charles R. F. 1937-2018 Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4120861-4 |
| title | Algebraic topology |
| title_auth | Algebraic topology |
| title_exact_search | Algebraic topology |
| title_full | Algebraic topology C. R. F. Maunder* |
| title_fullStr | Algebraic topology C. R. F. Maunder* |
| title_full_unstemmed | Algebraic topology C. R. F. Maunder* |
| title_short | Algebraic topology |
| title_sort | algebraic topology |
| topic | Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Algebraische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001845217&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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