The index theorem and the heat equation method:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2001
|
| Series: | Nankai tracts in mathematics
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 279-282) and index |
| Physical Description: | XIX, 287 S. |
| ISBN: | 9810246102 |
Staff View
MARC
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| 245 | 1 | 0 | |a The index theorem and the heat equation method |c Yanlin Yu |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2001 | |
| 300 | |a XIX, 287 S. | ||
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| 490 | 1 | |a Nankai tracts in mathematics |v 2 | |
| 500 | |a Includes bibliographical references (p. 279-282) and index | ||
| 650 | 4 | |a Atiyah-Singer index theorem | |
| 650 | 4 | |a Heat equation | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE v
DEFINITIONS AND FORMULAS ix
CHAPTER 1 PRELIMINARIES IN RIEMANNIAN GEOMETRY.... 1
1.1 Basic Notions of Riemannian Geometry 1
1.2 Computations by using Orthonormal Moving Frame 11
1.3 Differential Forms and Orthonormal Moving Frame Method 14
1.4 Classical Geometric Operators 23
1.5 Normal Coordinates 41
1.6 Computations on Sphere 60
1.7 Connections on Vector Bundles and Principal Bundles 70
1.8 General Tensor Calculus 78
CHAPTER 2 SCHRODINGER AND HEAT OPERATORS 83
2.1 Fundamental Solution and Levi Iteration 84
2.2 Existence of Fundamental Solution 89
2.3 Cauchy Problem of Heat Equation 94
2.4 Hodge Theorem 98
2.5 Applications of Hodge Theorem 106
2.6 Index Problem 112
CHAPTER 3 MP PARAMETRIX AND APPLICATIONS 115
3.1 MP Parametrix 115
3.2 Existence of Initial Solutions 119
3.3 Asymptotic Expansion for Heat Kernel 127
3.4 Local Index for Elliptic Operators 130
CHAPTER 4 CHERN WEIL THEORY 139
4.1 Characteristic Forms and Characteristic Classes 139
4.2 General Characteristic Forms 150
4.3 Chern Root Algorithm 162
4.4 Formal Approach to Local Index of Signature Operator 165
vii
viii CONTENTS
CHAPTER 5 CLIFFORD ALGEBRA AND SUPER ALGEBRA.... 175
5.1 Clifford Algebra 175
5.2 Super Algebra 183
5.3 Computations on Supertraces 190
CHAPTER 6 DIRAC OPERATOR 195
6.1 Spin Structure 195
6.2 Spinor Bundle 201
6.3 Dirac Operator 203
6.4 Index of Dirac Operator 207
CHAPTER 7 LOCAL INDEX THEOREMS 213
7.1 Local Index Theorem for Dirac Operator 214
7.2 Local Index Theorem for Signature Operator 231
7.3 Local Index Theorem for de Rham Hodge Operator 241
CHAPTER 8 RIEMANN ROCH THEOREM 245
8.1 Hermitian Metric 245
8.2 Hermitian Connection 249
8.3 Riemann Roch Operator 259
8.4 Weitzenbock Formula 268
8.5 Index Theorem 273
8.6 Riemann Roch Operator in Complex Analysis 276
REFERENCES 279
INDEX 283
|
| any_adam_object | 1 |
| author | Yu, Yanlin |
| author_facet | Yu, Yanlin |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-search | 514/.74 514.74 |
| dewey-sort | 3514 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014017611 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:56:12Z |
| institution | BVB |
| isbn | 9810246102 |
| language | English |
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| owner_facet | DE-19 DE-BY-UBM DE-384 DE-703 DE-355 DE-BY-UBR DE-11 DE-188 |
| physical | XIX, 287 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific |
| record_format | marc |
| series | Nankai tracts in mathematics |
| series2 | Nankai tracts in mathematics |
| spelling | Yu, Yanlin Verfasser aut The index theorem and the heat equation method Yanlin Yu Singapore [u.a.] World Scientific 2001 XIX, 287 S. txt rdacontent n rdamedia nc rdacarrier Nankai tracts in mathematics 2 Includes bibliographical references (p. 279-282) and index Atiyah-Singer index theorem Heat equation Wärmeleitungsgleichung (DE-588)4188859-5 gnd rswk-swf Indextheorem (DE-588)4140055-0 gnd rswk-swf Indextheorem (DE-588)4140055-0 s Wärmeleitungsgleichung (DE-588)4188859-5 s DE-604 Nankai tracts in mathematics 2 (DE-604)BV014017593 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009597807&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yu, Yanlin The index theorem and the heat equation method Nankai tracts in mathematics Atiyah-Singer index theorem Heat equation Wärmeleitungsgleichung (DE-588)4188859-5 gnd Indextheorem (DE-588)4140055-0 gnd |
| subject_GND | (DE-588)4188859-5 (DE-588)4140055-0 |
| title | The index theorem and the heat equation method |
| title_auth | The index theorem and the heat equation method |
| title_exact_search | The index theorem and the heat equation method |
| title_full | The index theorem and the heat equation method Yanlin Yu |
| title_fullStr | The index theorem and the heat equation method Yanlin Yu |
| title_full_unstemmed | The index theorem and the heat equation method Yanlin Yu |
| title_short | The index theorem and the heat equation method |
| title_sort | the index theorem and the heat equation method |
| topic | Atiyah-Singer index theorem Heat equation Wärmeleitungsgleichung (DE-588)4188859-5 gnd Indextheorem (DE-588)4140055-0 gnd |
| topic_facet | Atiyah-Singer index theorem Heat equation Wärmeleitungsgleichung Indextheorem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009597807&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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