Moduli Spaces of Riemannian Metrics

This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Tuschmann, Wilderich (Autor), Wraith, David J. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Basel : Springer Basel : Imprint: Birkhäuser, 2015.
Edición:1st ed. 2015.
Colección:Oberwolfach Seminars, 46
Temas:
Geometry, Differential.
Algebraic topology.
Manifolds (Mathematics).
Differential Geometry.
Algebraic Topology.
Manifolds and Cell Complexes.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Part I: Positive scalar curvature
  • The (moduli) space of all Riemannian metrics
  • Clifford algebras and spin
  • Dirac operators and index theorems
  • Early results on the space of positive scalar curvature metrics
  • Kreck-Stolz invariants
  • Applications of Kreck-Stolz invariants
  • The eta invariant and applications
  • The case of dimensions 2 and 3
  • The observer moduli space and applications
  • Other topological structures
  • Negative scalar and Ricci curvature
  • Part II: Sectional curvature
  • Moduli spaces of compact manifolds with positive or non-negative sectional curvature
  • Moduli spaces of compact manifolds with negative and non-positive sectional curvature
  • Moduli spaces of non-compact manifolds with non-negative sectional curvature
  • Positive pinching and the Klingenberg-Sakai conjecture.

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