Algebraic topology: a first course

Cover ......Page 1
Title page ......Page 2
Date-line ......Page 3
CONTENTS ......Page 4
Preface ......Page 6
Part I. Elementary Homotopy Theory ......Page 11
Introduction to Part I ......Page 13
1. Arrangement of Part I ......Page 15
2. Homotopy of Paths ......Page 16
3. Homotopy of Maps ......Page 21
4. Fundamental Group of the Circle ......Page 26
5. Covering Spaces ......Page 31
6. A Lifting Criterion ......Page 36
7. Loop Spaces and Higher Homotopy Groups ......Page 42
Part II. Singular Homology Theory ......Page 47
Introduction to Part II ......Page 49
8. Affine Preliminaries ......Page 51
9. Singular Theory ......Page 54
10. Chain Complexes ......Page 62
11. Homotopy Invariance of Homology ......Page 69
12. Relation Between $\pi_1$ and $H_1$ ......Page 73
13. Relative Homology ......Page 80
14. The Exact Homology Sequence ......Page 85
15. The Excision Theorem ......Page 92
16. Further Applications to Spheres ......Page 104
17. Mayer-Vietoris Sequence ......Page 108
18. The Jordan-Brouwer Separation Theorem ......Page 116
19. Construction of Spaces: Spherical Complexes ......Page 122
20. Betti Numbers and Euler Characteristic ......Page 138
21. Construction of Spaces: Cell Complexes and More Adjunction Spaces ......Page 144
Part III. Orientation and Duality on Manifolds ......Page 163
Introduction to Part III ......Page 165
22. Orientation of Manifolds ......Page 167
23. Singular Cohomology ......Page 184
24. Cup and Cap Products ......Page 205
25. Algebraic Limits ......Page 218
26. Poincare Duality ......Page 225
27. Alexander Duality ......Page 240
28. Lefschetz Duality ......Page 247
Part IV. Products and Lefschetz Fixed Point Theorem ......Page 257
Introduction to Part IV ......Page 259
29. Products ......Page 261
30. Thorn Class and Lefschetz Fixed Point Theorem ......Page 286
31. Intersection Numbers and Cup Products ......Page 300
Table of Symbols ......Page 311
Bibliography ......Page 313
Index ......Page 319