Moduli Spaces of Riemannian Metrics

  • Wilderich Tuschmann
  • David J. Wraith

Part of the Oberwolfach Seminars book series (OWS, volume 46)

Table of contents

  1. Front Matter
    Pages I-X
  2. Wilderich Tuschmann, David J. Wraith
    Pages 1-6
  3. Wilderich Tuschmann, David J. Wraith
    Pages 7-16
  4. Wilderich Tuschmann, David J. Wraith
    Pages 17-25
  5. Wilderich Tuschmann, David J. Wraith
    Pages 27-36
  6. Wilderich Tuschmann, David J. Wraith
    Pages 37-47
  7. Wilderich Tuschmann, David J. Wraith
    Pages 49-58
  8. Wilderich Tuschmann, David J. Wraith
    Pages 59-69
  9. Wilderich Tuschmann, David J. Wraith
    Pages 71-87
  10. Wilderich Tuschmann, David J. Wraith
    Pages 89-92
  11. Wilderich Tuschmann, David J. Wraith
    Pages 93-98
  12. Wilderich Tuschmann, David J. Wraith
    Pages 99-101
  13. Back Matter
    Pages 103-123

About this book

Introduction

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.

Keywords

Riemannian metrics curvature manifolds moduli spaces topology

Authors and affiliations

  • Wilderich Tuschmann
    • 1
  • David J. Wraith
    • 2
  1. 1.Institute for Algebra and GeometryKarlsruher Institut für Technologie KITKarlsruheGermany
  2. 2.Department of Mathematics and StatiNational University of IrelandMaynoothIreland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0948-1
  • Copyright Information Springer Basel 2015
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0947-4
  • Online ISBN 978-3-0348-0948-1
  • Series Print ISSN 1661-237X
  • Series Online ISSN 2296-5041
  • About this book
Industry Sectors
Aerospace
Oil, Gas & Geosciences