書誌事項

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

タイトル別名

指数定理

Index theorem. 1

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注記

Translation of: 指数定理, 1

Originally published: Tokyo : Iwanami Shoten, 1999

Includes bibliographical footnotes and index

内容説明・目次

内容説明

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.

目次

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.

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詳細情報

  • NII書誌ID(NCID)
    BA84170517
  • ISBN
    • 9780821820971
  • LCCN
    2007060301
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 原本言語コード
    jpn
  • 出版地
    Providence, R.I.
  • ページ数/冊数
    xvii, 205 p.
  • 大きさ
    22 cm
  • 分類
  • 件名
  • 親書誌ID
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