Seminar on the Atiyah-Singer Index Theorem
1st Edition
Published on 20. June 2016
376 pages
978-1-4008-8204-5 (ISBN)
Description
A classic treatment of the Atiyah-Singer index theorem from the acclaimed Annals of Mathematics Studies series
Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century.
To mark the continued success of the series, all books are available in paperback and as ebooks.
Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century.
To mark the continued success of the series, all books are available in paperback and as ebooks.
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Richard S. Palais
Seminar on the Atiyah-Singer Index Theorem
Book
09/1965
Princeton University Press
€104.40
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Person
Edited by Richard S. Palais
Content
Frontmatter, pg. i
CONTENTS, pg. v
PREFACE, pg. ix
CHAPTER I. STATEMENT OF THE THEOREM OUTLINE OF THE PROOF, pg. 1
CHAPTER II. REVIEW OF K-THEORY, pg. 13
CHAPTER III. THE TOPOLOGICAL INDEX OF AN OPERATOR ASSOCIATED TO A G-STRUCTURE, pg. 27
CHAPTER IV. DIFFERENTIAL OPERATORS ON VECTOR BUNDLES, pg. 51
CHAPTER V. ANALYTICAL INDICES OF SOME CONCRETE OPERATORS, pg. 95
CHAPTER VI. REVIEW OF FUNCTIONAL ANALYSIS, pg. 107
CHAPTER VII. FREDHDIM OPERATORS, pg. 119
CHAPTER VIII. CHAINS OP HILBERTIAN SPACES, pg. 125
CHAPTER IX. THE DISCRETE SOBOLEV CHAIN OF A VECTOR BUNDLE, pg. 147
CHAPTER X. THE CONTINUOUS SOBOLEV CHAIN OF A VECTOR BUNDLE, pg. 155
CHAPTER XI. THE SEELEY ALGEBRA, pg. 175
CHAPTER XII. HOMOTOPY INVARIANCE OF THE INDEX, pg. 185
CHAPTER XIII. WHITNEY SUMS, pg. 191
CHAPTER XIV. TENSOR PRODUCTS, pg. 197
CHAPTER XV. DEFINITION OF ia AND it ON K(M), pg. 215
CHAPTER XVI. CONSTRUCTION OF Intk, pg. 235
CHAPTER XVII. COBORDISM INVARIANCE OP THE ANALYTICAL INDEX, pg. 285
CHAPTER XVIII. BORDISM GROUPS OF BUNDLES, pg. 303
CHAPTER XIX. THE INDEX THEOREM: APPLICATIONS, pg. 313
APPENDIX I. THE INDEX THEOREM FOR MANIFOLDS WITH BOUNDARY, pg. 337
APPENDIX II. NON-STABLE CHARACTERISTIC CLASSES AND THE TOPOLOGICAL INDEX OP CLASSICAL ELLIPTIC OPERATORS, pg. 353
Backmatter, pg. 368
CONTENTS, pg. v
PREFACE, pg. ix
CHAPTER I. STATEMENT OF THE THEOREM OUTLINE OF THE PROOF, pg. 1
CHAPTER II. REVIEW OF K-THEORY, pg. 13
CHAPTER III. THE TOPOLOGICAL INDEX OF AN OPERATOR ASSOCIATED TO A G-STRUCTURE, pg. 27
CHAPTER IV. DIFFERENTIAL OPERATORS ON VECTOR BUNDLES, pg. 51
CHAPTER V. ANALYTICAL INDICES OF SOME CONCRETE OPERATORS, pg. 95
CHAPTER VI. REVIEW OF FUNCTIONAL ANALYSIS, pg. 107
CHAPTER VII. FREDHDIM OPERATORS, pg. 119
CHAPTER VIII. CHAINS OP HILBERTIAN SPACES, pg. 125
CHAPTER IX. THE DISCRETE SOBOLEV CHAIN OF A VECTOR BUNDLE, pg. 147
CHAPTER X. THE CONTINUOUS SOBOLEV CHAIN OF A VECTOR BUNDLE, pg. 155
CHAPTER XI. THE SEELEY ALGEBRA, pg. 175
CHAPTER XII. HOMOTOPY INVARIANCE OF THE INDEX, pg. 185
CHAPTER XIII. WHITNEY SUMS, pg. 191
CHAPTER XIV. TENSOR PRODUCTS, pg. 197
CHAPTER XV. DEFINITION OF ia AND it ON K(M), pg. 215
CHAPTER XVI. CONSTRUCTION OF Intk, pg. 235
CHAPTER XVII. COBORDISM INVARIANCE OP THE ANALYTICAL INDEX, pg. 285
CHAPTER XVIII. BORDISM GROUPS OF BUNDLES, pg. 303
CHAPTER XIX. THE INDEX THEOREM: APPLICATIONS, pg. 313
APPENDIX I. THE INDEX THEOREM FOR MANIFOLDS WITH BOUNDARY, pg. 337
APPENDIX II. NON-STABLE CHARACTERISTIC CLASSES AND THE TOPOLOGICAL INDEX OP CLASSICAL ELLIPTIC OPERATORS, pg. 353
Backmatter, pg. 368
