Moduli Spaces of Riemannian Metrics

Know about the book -

Moduli Spaces of Riemannian Metrics is written by Wilderich Tuschmann and published by Springer. It's available with International Standard Book Number or ISBN identification 3034809484 (ISBN 10) and 9783034809481 (ISBN 13).

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.