Moduli Spaces of Riemannian Metrics

• Main Authors: Tuschmann, Wilderich (Author), Wraith, David J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhäuser, 2015.
• Series: Oberwolfach Seminars, 46
• Subjects: Mathematics.; Differential geometry.; Algebraic topology.; Manifolds (Mathematics).; Complex manifolds.; Differential Geometry.; Algebraic Topology.; Manifolds and Cell Complexes (incl. Diff.Topology).

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...

Table of Contents:

• 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.