Seminar on the Atiyah-Singer index theorem /

This book consists mainly of slightly revised notes of a seminar held at the Institute for Advanced Study in 1963-64 upon the initiative of A. Borel. Aside from going through the details of the proof of the Index Theorem, the major emphasis of the seminar was placed on developing the topological and...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Palais, Richard S., Atiyah, Michael Francis, 1929-2019 (Autor), Borel, Armand (Autor), Floyd, E. E. (Edwin Earl) (Autor), Seeley, Robert T. (Autor), Shih, Weishu (Autor), Solovay, Robert M. (Autor)
Autor Corporativo: Institute for Advanced Study (Princeton, N.J.)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, N.J. : Princeton University Press, 1965.
Colección:Annals of mathematics studies ; no. 57.
Temas:
Atiyah-Singer index theorem.
Differential topology.
Homology theory.
Topologie différentielle.
Homologie.
Théorème d'Atiyah-Singer.
MATHEMATICS > Topology.
Indextheorem
Instructional and educational works
Instructional and educational works.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Statement of the theorem : outline of the proof / A. Borel
  • Review of K-theory / Robert Solovay
  • The topological index of an operator associated to a G-structure / Robert Solovay
  • Differential operators on vector bundles / Richard S. Palais
  • Analytical indices of some concrete operators / Robert M. Solovay
  • Review of functional analysis / Richard S. Palais
  • Fredhold operators / Richard S. Palais
  • Chains of Hilbertian spaces / Richard S. Palais
  • The discrete Sobolev chain of a vector bundle / Richard S. Palais
  • The continuous Sobolev chain of a vector bundle / Richard S. Palais
  • The Seeley algebra / Richard S. Palais
  • Homotopy invariance of the index / Richard S. Palais
  • Whitney sums / Richard S. Palais
  • Tensor products / Richard S. Palais
  • Definition of [lowercase]i[subscript lowercase]a and [lowercase]i[subscript lowercase]t on K(M) / Robert M. Solovay
  • Construction of Int[subscript lowercase]k / R. S. Palais and R. T. Seeley
  • Cobordism invariance of the analytical index / R. S. Palais and R. T. Seeley
  • Bordism groups of bundles / E. E. Floyd
  • The index theorem : applications / Robert M. Solovay
  • Appendix I. The index theorem for manifolds with boundary / M. F. Atiyah
  • Appendix II. Non-stable characteristic classes and the topological index of classical elliptic operators / Weishu Shih.

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