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Moduli Spaces of Riemannian Metrics

Moduli Spaces of Riemannian Metrics by Wilderich Tuschmann
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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.
Springer Basel; October 2015
127 pages; ISBN 9783034809481
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Title: Moduli Spaces of Riemannian Metrics
Author: Wilderich Tuschmann; David J. Wraith
 
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9783034809474
9783034809481