Homotopy Theory: An Introduction to Algebraic Topology (eBook)

Front Cover 1
Homotopy Theory: An Introduction to Algebraic Topology 4
Copyright Page 5
Contents 6
Preface 8
List of Symbols 12
Chapter 0. Preliminaries 16
Chapter 1. Some Simple Topological Spaces 19
Chapter 2. Some Simple Topological Problems 24
Chapter 3. Homotopy Theory 28
Chapter 4. Category Theory 32
Chapter 5. The Fundamental Group 37
Chapter 6. More on the Fundamental Group 44
Chapter 7. Calculating the Fundamental Group 49
Chapter 8. A Convenient Category of Topological Spaces 65
Chapter 9. Track Groups and Homotopy Groups 77
Chapter 10. Relative Homotopy Groups 85
Chapter 11. Locally Trivial Bundles 92
Chapter 12. Simplicial Complexes and Linearity 105
Chapter 13. Calculating Homotopy Groups: The Blakers–Massey Theorem 114
Chapter 14. The Topology of CW Complexes 128
Chapter 15. Limits 137
Chapter 16. The Homotopy Theory of CW Complexes 145
Chapter 17. K(p, n)’s and Postnikov Systems 172
Chapter 18. Spectral Reduced Homology and Cohomology Theories 183
Chapter 19. Spectral Unreduced Homology and Cohomology Theories 198
Chapter 20. Ordinary Homology of CW Complexes 202
Chapter 21. Homology and Cohomology Groups of More General Spaces 215
Chapter 22. The Relation between Homotopy and Ordinary Homology 230
Chapter 23. Multiplicative Structure 236
Chapter 24. Relations between Chain Complexes 260
Chapter 25. Homological Algebra over a Principal Ideal Domain: Künneth and Universal Coefficient Theorems 271
Chapter 26. Orientation and Duality 284
Chapter 27. Cohomology Operations 309
Chapter 28. Adem Relations 325
Chapter 29. K-Theories 339
Chapter 30. Cobordism 357
References 375
Index 378