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自旋几何【2025|PDF下载-Epub版本|mobi电子书|kindle百度云盘下载】

自旋几何
  • （美）劳森（LAWSON，H.B）著 著
  • 出版社： 世界图书出版公司北京公司
  • ISBN：7510029639
  • 出版时间：2011
  • 标注页数：428页
  • 文件大小：67MB
  • 文件页数：442页
  • 主题词：

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图书目录

INTRODUCTION3

CHAPTER Ⅰ Clifford Algebras，Spin Groups and Their Representations7

1．Clifford algebras7

2．The groups Pin and Spin12

3．The algebras Clnand Clr,s20

4．The classification25

5．Representations30

6．Lie algebra structures40

7．Some direct applications to geometry44

8．Some further applications to the theory of Lie groups49

9．K-theory and the Atiyah-Bott-Shapiro construction58

10．KR-theory and the (1,1)-Periodicity Theorem70

CHAPTER Ⅱ Spin Geometry and the Dirac Operators77

1．Spin structures on vector bundles78

2．Spin manifolds and spin cobordism85

3．Clifford and spinor bundles93

4．Connections on spinor bundles101

5．The Dirac operators112

6．The fundamental elliptic operators135

7．Clk-linear Dirac operators139

8．Vanishing theorems and some applications153

CHAPTER Ⅲ Index Theorems166

1．Differential operators167

2．Sobolev spaces and Sobolev theorems170

3．Pseudodifferential operators177

4．Elliptic operators and parametrices188

5．Fundamental results for elliptic operators192

6．The heat kernel and the index198

7．The topological invariance of the index201

8．The index of a family of elliptic operators205

9．The G-index211

10．The Clifford index214

11．Multiplicative sequences and the Chern character225

12．Thom isomorphisms and the Chern character defect238

13．The Atiyah-Singer Index Theorem243

14．Fixed-point formulas for elliptic operators259

15．The Index Theorem for Families268

16．Families of real operators and the Clk-index Theorem270

17．Remarks on heat and supersymmetry277

CHAPTER Ⅳ Applications in Geometry and Topology278

1．Integrality theorems280

2．Immersions of manifolds and the vector field problem281

3．Group actions on manifolds291

4．Compact manifolds of positive scalar curvature297

5．Positive scalar curvature and the fundamental group302

6．Complete manifolds of positive scalar curvature313

7．The topology of the space of positive scalar curvature metrics326

8．Clifford multiplication and K？hler manifolds330

9．Pure spinors,complex structures，and twistors335

10．Reduced holonomy and calibrations345

11．Spinor cohomology and complex manifolds with vanishing first Chern class357

12．The Positive Mass Conjecture in general relativity368

APPENDIX A Principal G-bundles370

APPENDIX B Classifying Spaces and Characteristic Classes376

APPENDIX C Orientation Classes and Thom Isomorphisms in K-theory384

APPENDIX D Spinc-manifolds390

BIBLIOGRAPHY402

INDEX417

NOTATION INDEX425

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