Algebraic topology

Cover
......Page 1
Title
......Page 2
Contents
......Page 3
Preface
......Page 6
0. Some underlying geometric notions
......Page 10
1. The fundamental group
......Page 30
1.1 Basic constructions
......Page 34
1.2 Van Kampen's theorem
......Page 49
1.3 Covering spaces
......Page 65
1.A Graphs and free groups
......Page 92
1.B K(G,1) spaces and graphs of groups
......Page 96
2. Homology
......Page 106
2.1 Simplicial and singular homology
......Page 111
2.2 Computations and applications
......Page 143
2.3 The formal viewpoint
......Page 169
2.A Homology and fundamental group
......Page 175
2.B Classical applications
......Page 178
2.C Simplicial approximation
......Page 186
3. Cohomology
......Page 194
3.1 Cohomology groups
......Page 199
3.2 Cup product
......Page 215
3.3 Poincaré duality
......Page 239
3.A Universal coefficients for homology
......Page 270
3.B The general Kuenneth formula
......Page 277
3.C H-spaces and Hopf algebras
......Page 290
3.D The cohomology of SO(n)
......Page 301
3.E Bockstein homomorphisms
......Page 312
3.F Limits and Ext
......Page 320
3.G Transfer homomorphisms
......Page 330
3.H Local coefficients
......Page 336
4. Homotopy theory
......Page 346
4.1 Homotopy groups
......Page 348
4.2 Elementary methods of calculation
......Page 369
4.3 Connections with cohomology
......Page 402
4.A Basepoints and homotopy
......Page 430
4.B The Hopf invariant
......Page 436
4.C Minimal cell structures
......Page 438
4.D Cohomology of fiber bundles
......Page 440
4.E The Brown representability theorem
......Page 457
4.F Spectra and homology theories
......Page 461
4.G Gluing constructions
......Page 465
4.H Eckmann-Hilton duality
......Page 469
4.I Stable splittings of spaces
......Page 475
4.J The loopspace of a suspension
......Page 479
4.K The Dold-Thom theorem
......Page 484
4.L Steenrod squares and powers
......Page 496
Appendix
......Page 528
Bibliography
......Page 542
Index
......Page 548