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Softcover ISBN:  9780821820971 
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Softcover ISBN:  9780821820971 
Product Code:  MMONO/235 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470447892 
Product Code:  MMONO/235.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821820971 
eBook ISBN:  9781470447892 
Product Code:  MMONO/235.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsIwanami Series in Modern MathematicsVolume: 235; 2007; 205 ppMSC: Primary 58
The AtiyahSinger 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, Ktheory, 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.

Table of Contents

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


Additional Material

Reviews

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 AtiyahSinger 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, Ktheory, 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