Moduli Spaces of Riemannian Metrics by Wilderich TuschmannModuli Spaces of Riemannian Metrics by Wilderich Tuschmann

Moduli Spaces of Riemannian Metrics

byWilderich Tuschmann, David J. Wraith

Paperback | February 5, 2016

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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 and non-positive sectional curvature. If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research.
Wilderich Tuschmann's general research interests lie in the realms of global differential geometry, Riemannian geometry, geometric topology, and their applications, including, for example, questions concerning the geometry and topology of nonnegative and almost nonnegative curvature, singular metric spaces, collapsing and Gromov-Hausdo...
Title:Moduli Spaces of Riemannian MetricsFormat:PaperbackDimensions:123 pagesPublished:February 5, 2016Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034809476

ISBN - 13:9783034809474


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.

Editorial Reviews

"This book serves as a comprehensive (yet succinct and accessible) guide to the topology of spaces of Riemannian metrics with a given curvature sign condition. . This is one of the most well-studied aspects of moduli spaces of Riemannian metrics but remains a very active area of research, and the reader will find in this book the current state-of-the-art results on the subject." (Renato G. Bettiol, Mathematical Reviews, October, 2016)"The interplay between analysis, geometry, and topology is clearly laid out in this book; analytic invariants are constructed to elucidate the structure of geometric moduli spaces. The book is an elegant and concise introduction to the field that puts a number of discrete papers into a coherent focus. . A useful bibliography of the subject appears at the end." (Peter B. Gilkey, zbMATH 1336.53002, 2016)