
SoftcoverISBN: | 978-0-8218-2097-1 |
Product Code: | MMONO/235 |
List Price: | $45.00 |
MAA Member Price: | $40.50 |
AMS Member Price: | $36.00 |
eBookISBN: | 978-1-4704-4789-2 |
Product Code: | MMONO/235.E |
List Price: | $42.00 |
MAA Member Price: | $37.80 |
AMS Member Price: | $33.60 |
SoftcoverISBN: | 978-0-8218-2097-1 |
eBookISBN: | 978-1-4704-4789-2 |
Product Code: | MMONO/235.B |
List Price: | $87.00$66.00 |
MAA Member Price: | $78.30$59.40 |
AMS Member Price: | $69.60$52.80 |

Softcover ISBN: | 978-0-8218-2097-1 |
Product Code: | MMONO/235 |
List Price: | $45.00 |
MAA Member Price: | $40.50 |
AMS Member Price: | $36.00 |
eBook ISBN: | 978-1-4704-4789-2 |
Product Code: | MMONO/235.E |
List Price: | $42.00 |
MAA Member Price: | $37.80 |
AMS Member Price: | $33.60 |
Softcover ISBN: | 978-0-8218-2097-1 |
eBookISBN: | 978-1-4704-4789-2 |
Product Code: | MMONO/235.B |
List Price: | $87.00$66.00 |
MAA Member Price: | $78.30$59.40 |
AMS Member Price: | $69.60$52.80 |
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Book DetailsTranslations of Mathematical MonographsIwanami Series in Modern MathematicsVolume: 235; 2007; 205 ppMSC: Primary 58;
The Atiyah-Singer index theorem is a remarkable result that allows one to compute the space of solutions of a linear elliptic partial differential operator on a manifold in terms of purely topological data related to the manifold and the symbol of the operator. First proved by Atiyah and Singer in 1963, it marked the beginning of a completely new direction of research in mathematics with relations to differential geometry, partial differential equations, differential topology, K-theory, physics, and other areas.
The author's main goal in this volume is to give a complete proof of the index theorem. The version of the proof he chooses to present is the one based on the localization theorem. The prerequisites include a first course in differential geometry, some linear algebra, and some facts about partial differential equations in Euclidean spaces.ReadershipGraduate students interested in index theory.
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Table of Contents
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Chapters
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Prelude
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Manifolds, vector bundles and elliptic complexes
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Index and its localization
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Examples of the localization of the index
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Localization of eigenfunctions of the operator of Laplace type
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Formulation and proof of the index theorem
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Characteristic classes
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Additional Material
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Reviews
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The book is well organized... The strategy of the proof and applications are clearly laid out. ...this monograph is an important contribution to the subject.
Mathematical Reviews
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The Atiyah-Singer index theorem is a remarkable result that allows one to compute the space of solutions of a linear elliptic partial differential operator on a manifold in terms of purely topological data related to the manifold and the symbol of the operator. First proved by Atiyah and Singer in 1963, it marked the beginning of a completely new direction of research in mathematics with relations to differential geometry, partial differential equations, differential topology, K-theory, physics, and other areas.
The author's main goal in this volume is to give a complete proof of the index theorem. The version of the proof he chooses to present is the one based on the localization theorem. The prerequisites include a first course in differential geometry, some linear algebra, and some facts about partial differential equations in Euclidean spaces.
Graduate students interested in index theory.
-
Chapters
-
Prelude
-
Manifolds, vector bundles and elliptic complexes
-
Index and its localization
-
Examples of the localization of the index
-
Localization of eigenfunctions of the operator of Laplace type
-
Formulation and proof of the index theorem
-
Characteristic classes
-
The book is well organized... The strategy of the proof and applications are clearly laid out. ...this monograph is an important contribution to the subject.
Mathematical Reviews