Basic algebraic topology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton u.a.
CRC Press
2014
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 535 S. |
| ISBN: | 9781466562431 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804151449012142080 |
|---|---|
| adam_text | Titel: Basic algebraic topology
Autor: Śāstri, Anant R
Jahr: 2014
Contents
Foreword vii
Preface ix
List of Symbols and Abbreviations xiii
Sectionwise Dependence Tree xv
1 Introduction 1
1.1 The Basic Problem 1
1.2 Fundamental Group 12
1.3 Function Spaces and Quotient Spaces 22
1.4 Relative Homotopy 26
1.5 Some Typical Constructions 29
1.6 Cofibrations 36
1.7 Fibrations 41
1.8 Categories and Functors 44
1.9 Miscellaneous Exercises to Chapter 1 54
2 Cell Complexes and Simplicial Complexes 63
2.1 Basics of Convex Polytopes 63
2.2 Cell Complexes 82
2.3 Product of Cell Complexes • 89
2.4 Homotopical Aspects 94
2.5 Cellular Maps 96
2.6 Abstract Simplicial Complexes 98
2.7 Geometric Realization of Simplicial Complexes 100
2.8 Barycentric Subdivision 108
2.9 Simplicial Approximation 113
2.10 Links and Stars 121
2.11 Miscellaneous Exercises to Chapter 2 122
3 Covering Spaces and Fundamental Group 127
3.1 Basic Definitions 127
3.2 Lifting Properties 130
3.3 Relation with the Fundamental Group 132
3.4 Classification of Covering Projections 135
3.5 Group Action 143
3.6 Pushouts and Free Products 153
3.7 Seifert-van Kampen Theorem 157
3.8 Applications 159
3.9 Miscellaneous Exercises to Chapter 3 165
iii
iv
4 Homology Groups 169
4.1 Basic Homological Algebra 169
4.2 Singular Homology Groups 177
4.3 Construction of Some Other Homology Groups 187
4.4 Some Applications of Homology 198
4.5 Relation between 7ri and Hi 204
4.6 All Postponed Proofs 206
4.7 Miscellaneous Exercises to Chapter 4 211
5 Topology of Manifolds 213
5.1 Set Topological Aspects 213
5.2 Triangulation of Manifolds 221
5.3 Classification of Surfaces 229
5.4 Basics of Vector Bundles 240
5.5 Miscellaneous Exercises to Chapter 5 251
6 Universal Coefficient Theorem for Homology 253
6.1 Method of Acyclic Models 253
6.2 Homology with Coefficients: The Tor Functor 257
6.3 Kunneth Formula 263
6.4 Miscellaneous Exercises to Chapter 6 271
7 Cohomology 273
7.1 Cochain Complexes 273
7.2 Universal Coefficient Theorem for Cohomology 275
7.3 Products in Cohomology 281
7.4 Some Computations 285
7.5 Cohomology Operations; Steenrod Squares 292
8 Homology of Manifolds 303
8.1 Orientability 303
8.2 Duality Theorems 311
8.3 Some Applications 320
8.4 de R.ham Cohomology 324
8.5 Miscellaneous Exercises to Chapter 8 327
9 Cohomology of Sheaves 329
9.1 Sheaves 329
9.2 Injective Sheaves and Resolutions 340
9.3 Cohomology of Sheaves 346
9.4 Cech Cohomology 350
9.5 Miscellaneous Exercises to Chapter 9 356
10 Homotopy Theory 357
10.1 iL-spaces and H -spaces 357
10.2 Higher Homotopy Groups 362
10.3 Change of Base Point 370
10.4 The Hurewicz Isomorphism 375
10.5 Obstruction Theory 384
10.6 Homotopy Extension and Classification 387
10.7 Eilenberg-Mac Lane Spaces 391
10.8 Moore-Postnikov Decomposition 396
10.9 Computation with Lie Groups and Their Quotients 403
10.10 Homology with Local Coefficients 411
10.11 Miscellaneous Exercises to Chapter 10 414
11 Homology of Fibre Spaces 415
11.1 Generalities about Fibrations 415
11.2 Thom Isomorphism Theorem 422
11.3 Fibrations over Suspensions 430
11.4 Cohomology of Classical Groups 436
11.5 Miscellaneous Exercises to Chapter 11 444
12 Characteristic Classes 445
12.1 Orientation and Euler Class 445
12.2 Construction of Steifel-Whitney Classes and Chern Classes . 452
12.3 Fundamental Properties 454
12.4 Splitting Principle and Uniqueness 457
12.5 Complex Bundles and Pontrjagin Classes 458
12.6 Miscellaneous Exercises to Chapter 12 461
13 Spectral Sequences 463
13.1 Warm-up 463
13.2 Exact Couples 465
13.3 Algebra of Spectral Sequences 470
13.4 Leray-Serre Spectral Sequence 475
13.5 Some Immediate Applications 480
13.6 Transgression 484
13.7 Cohomology Spectral Sequences 486
13.8 Serre Classes 491
13.9 Homotopy Groups of Spheres 497
Hints and Solutions 501
Bibliography 525
Index
531
|
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| spelling | Śāstri, Anant R. Verfasser (DE-588)1013824709 aut Basic algebraic topology Anant R. Shastri Boca Raton u.a. CRC Press 2014 XV, 535 S. txt rdacontent n rdamedia nc rdacarrier Algebraic topology Algebraic topology / Problems, exercises, etc Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content 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=026811762&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Śāstri, Anant R. Basic algebraic topology Algebraic topology Algebraic topology / Problems, exercises, etc Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4120861-4 (DE-588)4123623-3 |
| title | Basic algebraic topology |
| title_auth | Basic algebraic topology |
| title_exact_search | Basic algebraic topology |
| title_full | Basic algebraic topology Anant R. Shastri |
| title_fullStr | Basic algebraic topology Anant R. Shastri |
| title_full_unstemmed | Basic algebraic topology Anant R. Shastri |
| title_short | Basic algebraic topology |
| title_sort | basic algebraic topology |
| topic | Algebraic topology Algebraic topology / Problems, exercises, etc Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Algebraic topology Algebraic topology / Problems, exercises, etc Algebraische Topologie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026811762&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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