Index Theorem 1 (Translations of Mathematical Monographs No. 235)
By: Mikio Furuta (author)Paperback
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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.
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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- ID: 9780821820971
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