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流形上的层 英文PDF|Epub|txt|kindle电子书版本网盘下载
- （日）柏原正树著 著
- 出版社： 北京;西安：世界图书出版公司出版社
- ISBN：9787510070303
- 出版时间：2014
- 标注页数：514页
- 文件大小：69MB
- 文件页数：524页
- 主题词：上同调论－英文
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图书目录
Introduction1
A Short History：Les débuts de la théorie des faisceaux by Christian Houzel7
Ⅰ．Homological algebra23
Summary23
1.1．Categories and functors23
1.2．Abelian categories26
1.3．Categories of complexes30
1.4．Mapping cones34
1.5．Triangulated categories38
1.6．Localization of categories41
1.7．Derived categories45
1.8．Derived functors50
1.9．Double complexes54
1.10．Bifunctors56
1.11．Ind-objects and pro-objects61
1.12．The Mittag-Leffler condition64
Exercises to Chapter Ⅰ69
Notes81
Ⅱ．Sheaves83
Summary83
2.1．Presheaves83
2.2．Sheaves85
2.3．Operations on sheaves90
2.4．Injective,flabby and flat sheaves98
2.5．Sheaves on locally compact spaces102
2.6．Cohomology of sheaves109
2.7．Some vanishing theorems116
2.8．Cohomology of coverings123
2.9．Examples of sheaves on real and complex manifolds125
Exercises to Chapter Ⅱ131
Notes138
Ⅲ．Poincaré-Verdier duality and Fourier-Sato transformation139
Summary139
3.1．Poincaré-Verdier duality140
3.2．Vanishing theorems on manifolds149
3.3．Orientation and duality151
3.4．Cohomologically constructible sheaves158
3.5．γ-topology161
3.6．Kernels164
3.7．Fourier-Sato transformation167
Exercises to Chapter Ⅲ178
Notes184
Ⅳ．Specialization and microlocalization185
Summary185
4.1．Normal deformation and normal cones185
4.2．Specialization190
4.3．Microlocalization198
4.4．The functor μhom201
Exercises to Chapter Ⅳ214
Notes215
Ⅴ．Micro-support of sheaves217
Summary217
5.1．Equivalent definitions of the micro-support218
5.2．Propagation222
5.3．Examples：micro-supports associated with locally closed subscts226
5.4．Functorial properties of the micro-support229
5.5．Micro-support of conic sheaves241
Exereises to Chapter Ⅴ245
Notes247
Ⅵ．Micro-support and microlocalization249
Summary249
6.1．The category Db（X；Ω）250
6.2．Normal cones in cotangent bundles258
6.3．Direct images263
6.4．Microlocalization268
6.5．Involutivity and propagation271
6.6．Sheaves in a neighborhood of an involutive manifold274
6.7．Microlocalization and inverse images275
Exercises to Chapter Ⅵ279
Notes281
Ⅶ．Contact transformations and pure sheaves283
Summary283
7.1．Microlocal kernels284
7.2．Contact transfornations for sheaves289
7.3．Microlocal composition of kernels293
7.4．Integral transformations for sheaves associated with submanifolds298
7.5．Pure sheaves309
Exercises to Chapter Ⅶ318
Notes318
Ⅷ．Constructible sheaves320
Summary320
8.1．Constructible sheaves on a simplicial complex321
8.2．Subanalytic sets327
8.3．Subanalytic isotropic sets and μ-stratifications328
8.4．R-constructible sheaves338
8.5．C-constructible sheaves344
8.6．Nearby-cycle functor and vanishing-cycle functor350
Exercises to Chapter Ⅷ356
Notes358
Ⅸ．Characteristic cycles360
Summary360
9.1．Index formula361
9.2．Subanalytic chains and subanalytic cycles366
9.3．Lagrangian cycles373
9.4．Characteristic cycles377
9.5．Microlocal index formulas384
9.6．Lefschetz fixed point formula389
9.7．Constructible functions and Lagrangian cycles398
Exercises to Chapter Ⅸ406
Notes409
Ⅹ．Perverse sheaves411
Summary411
10.1．t-structures411
10.2．Perverse sheaves on real manifolds419
10.3．Perverse sheaves on complex manifolds426
Exercises to Chapter Ⅹ438
Notes440
Ⅺ．Applications to O-modules and D-modules441
Summary441
11.1．The sheaf Ox442
11.2．Dx-modules445
11.3．Holomorphic solutions of Dx-modules453
11.4．Microlocal study of Ox459
11.5．Microfunctions466
Exercises to Chapter Ⅺ471
Notes474
Appendix：Symplectic geometry477
Summary477
A.1．Symplectic vector spaces477
A.2．Homogeneous symplectic manifolds481
A.3．Inertia index486
Exercises to the Appendix493
Notes495
Bibliography496
List of notations and conventions502
Index509