Coarse cohomology and index theory on complete Riemannian manifolds /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Roe, John, 1959- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island : American Mathematical Society, 1993.
Colección:Memoirs of the American Mathematical Society ; no. 497.
Temas:
Riemannian manifolds.
Homology theory.
Index theory (Mathematics)
Variétés de Riemann.
Homologie.
Théorie de l'index (Mathématiques)
Homology theory
Riemannian manifolds
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Contents
  • Chapter 1. Introduction
  • Chapter 2. Basic properties of coarse cohomology
  • 2.1. The uniformly bornologous categories
  • 2.2. Definition of coarse theory
  • 2.3. Examples
  • 2.4. Product structure on coarse theory
  • Chapter 3. Computation of coarse cohomology
  • 3.1. Review of Cech theory
  • 3.2. The main theorem
  • 3.3. Alternative definitions of coarse theory
  • 3.4. When is c an isomorphism?
  • 3.5. Bornotopy
  • 3.6. Examples
  • Chapter 4. Cyclic cohomology and index theory
  • 4.1. Operator algebras
  • 4.2. The Connes character map
  • ""4.3. Index theory""""4.4. The computation for R[sup(2m)]""; ""4.5. The general index theorem (even case)""; ""4.6. The odd case""; ""Chapter 5. Coarse cohomology and compactification""; ""5.1. Higson's corona space""; ""5.2. K[sub(*)](B[sub(H)]) and K[sub(*)](vM)""; ""5.3. The transgression map""; ""5.4. Relation to index theory""; ""Chapter 6. Examples and Applications""; ""6.1. Index theorem for partitioned manifolds""; ""6.2. Ultraspherical manifolds""; ""6.3. Application to positive scalar curvature""; ""6.4. Application to KÃ?hler manifolds""
  • 6.5. Applications to the signature operator6.6. Relation with the Novikov conjecture
  • References

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