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Index Theorem. 1
 
Mikio Furuta University of Tokyo, Tokyo, Japan
Index Theorem. 1
Softcover ISBN:  978-0-8218-2097-1
Product Code:  MMONO/235
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4789-2
Product Code:  MMONO/235.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-2097-1
eBook: ISBN:  978-1-4704-4789-2
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
Index Theorem. 1
Click above image for expanded view
Index Theorem. 1
Mikio Furuta University of Tokyo, Tokyo, Japan
Softcover ISBN:  978-0-8218-2097-1
Product Code:  MMONO/235
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4789-2
Product Code:  MMONO/235.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-2097-1
eBook ISBN:  978-1-4704-4789-2
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 Details
     
     
    Translations of Mathematical Monographs
    Iwanami Series in Modern Mathematics
    Volume: 2352007; 205 pp
    MSC: 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.

    Readership

    Graduate 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
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Iwanami Series in Modern Mathematics
Volume: 2352007; 205 pp
MSC: 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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.