Index theorem

Author(s)

• 古田, 幹雄 フルタ, ミキオ
• 小野, 薫 オノ, カオル

Bibliographic Information

Index theorem

Mikio Furuta ; translated by Kauro [i.e. Kaoru] Ono

（Translations of mathematical monographs, v. 235）（Iwanami series in modern mathematics）

American Mathematical Society, c2007

• 1

Other Title

指数定理

Index theorem. 1

Note

Translation of: 指数定理, 1

Originally published: Tokyo : Iwanami Shoten, 1999

Includes bibliographical footnotes and index

Description and Table of Contents

Description

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.

Table of Contents

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 Index.

by "Nielsen BookData"

Details

• NCID: BA84170517
• ISBN:
  • 9780821820971
• LCCN: 2007060301
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: jpn
• Place of Publication: Providence, R.I.
• Pages/Volumes: xvii, 205 p.
• Size: 22 cm
• Classification:
  • LCC : QA614.92
  • DC22 : 514/.74
• Subject Headings:
  • LCSH : Index theorems
• Parent Bibliography ID:
  • BA00080309
  • BA4365335X