ENGLISH

Moduli Spaces of Riemannian Metrics

By Wilderich Tuschmann , David J. Wraith

Book information

Publisher
Birkhäuser Basel
Year
2015
ISBN
3034809476, 978-3-0348-0947-4, 978-3-0348-0948-1
DOI
10.1007/978-3-0348-0948-1
Language
english
Format
PDF
Filesize
2 MB (1690948 bytes)
Series
Oberwolfach Seminars 46
Edition
2
Pages
127\127
Time added
2015-11-18 12:16:34
Differential Geometry; Algebraic Topology; Manifol

Description

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.

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