- 作 者：（美）布里登著
- 出 版 社：北京/西安：世界图书出版公司
- 出版年份：2010
- ISBN：9787510004698
- 标注页数：504 页
- PDF页数：515 页
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Ⅰ Sheaves and Presheaves 1
1 Definitions 1
2 Homomorphisms,subsheaves,and quotient sheaves 8
3 Direct and inverse images 12
4 Cohomomorphisms 14
5 Algebraic constructions 16
6 Supports 21
7 Classical cohomology theories 24
Exercises 30
Ⅱ Sheaf Cohomology 33
1 Differential sheaves and resolutions 34
2 The canonical resolution and sheaf cohomology 36
3 Injective sheaves 41
4 Acyclic sheaves 46
5 Flabby sheaves 47
6 Connected sequences of functors 52
7 Axioms for cohomology and the cup product 56
8 Maps of spaces 61
9 Ф-soft and Ф-fine sheaves 65
10 Subspaces 71
11 The Vietoris mapping theorem and homotopy invariance 75
12 Relative cohomology 83
13 Mayer-Vietoris theorems 94
14 Continuity 100
15 The Künneth and universal coefficient theorems 107
16 Dimension 110
17 Local connectivity 126
18 Change of supports;local cohomology groups 134
19 The transfer homomorphism and the Smith sequences 137
20 Steenrod's cyclic reduced powers 148
21 The Steenrod operations 162
Exercises 169
Ⅲ Comparison with Other Cohomology Theories 179
1 Singular cohomology 179
2 Alexander-Spanier cohomology 185
3 de Rham cohomology 187
4 ？ech cohomology 189
Exercises 194
Ⅳ Applications of Spectral Sequences 197
1 The spectral sequence of a differential sheaf 198
2 The fundamental theorems of sheaves 202
3 Direct image relative to a support family 210
4 The Leray sheaf 213
5 Extension of a support family by a family on the base space 219
6 The Leray spectral sequence of a map 221
7 Fiber bundles 227
8 Dimension 237
9 The spectral sequences of Borel and Cartan 246
10 Characteristic classes 251
11 The spectral sequence of a filtered differential sheaf 257
12 The Fary spectral sequence 262
13 Sphere bundles with singularities 264
14 The Oliver transfer and the Conner conjecture 267
Exercises 275
Ⅴ Borel-Moore Homology 279
1 Cosheaves 281
2 The dual of a differential cosheaf 289
3 Homology theory 292
4 Maps of spaces 299
5 Subspaces and relative homology 303
6 The Vietoris theorem,homotopy,and covering spaces 317
7 The homology sheaf of a map 322
8 The basic spectral sequences 324
9 Poincaré duality 329
10 The cap product 335
11 Intersection theory 344
12 Uniqueness theorems 349
13 Uniqueness theorems for maps and relative homology 358
14 The Künneth formula 364
15 Change of rings 368
16 Generalized manifolds 373
17 Locally homogeneous spaces 392
18 Homological fibrations and p-adic transformation groups 394
19 The transfer homomorphism in homology 403
20 Smith theory in homology 407
Exercises 411
Ⅵ Cosheaves and ？ech Homology 417
1 Theory of cosheaves 418
2 Local triviality 420
3 Local isomorphisms 421
4 ？ech homology 424
5 The reflector 428
6 Spectral sequences 431
7 Coresolutions 432
8 Relative ？ech homology 434
9 Locally paracompact spaces 438
10 Borel-Moore homology 439
11 Modified Borel-Moore homology 442
12 Singular homology 443
13 Acyclic coverings 445
14 Applications to maps 446
Exercises 448
A Spectral Sequences 449
1 The spectral sequence of a filtered complex 449
2 Double complexes 451
3 Products 453
4 Homomorphisms 454
B Solutions to Selected Exercises 455
Solutions for Chapter Ⅰ 455
Solutions for Chapter Ⅱ 459
Solutions for Chapter Ⅲ 472
Solutions for Chapter Ⅳ 473
Solutions for Chapter Ⅴ 480
Solutions for Chapter Ⅵ 486
Bibliography 487
List of Symbols 491
List of Selected Facts 493
Index 495