Manifolds with Cusps of Rank One

Spectral Theory and L2-Index Theorem

  • Authors
  • Werner Müller

Part of the Lecture Notes in Mathematics book series (LNM, volume 1244)

Table of contents

  1. Front Matter
    Pages I-X
  2. Werner Müller
    Pages 1-4
  3. Werner Müller
    Pages 5-12
  4. Werner Müller
    Pages 13-21
  5. Werner Müller
    Pages 22-30
  6. Werner Müller
    Pages 31-45
  7. Werner Müller
    Pages 46-59
  8. Werner Müller
    Pages 60-63
  9. Werner Müller
    Pages 64-73
  10. Werner Müller
    Pages 74-83
  11. Werner Müller
    Pages 84-99
  12. Werner Müller
    Pages 100-138
  13. Werner Müller
    Pages 139-149
  14. Back Matter
    Pages 150-158

About this book

Introduction

The manifolds investigated in this monograph are generalizations of (XX)-rank one locally symmetric spaces. In the first part of the book the author develops spectral theory for the differential Laplacian operator associated to the so-called generalized Dirac operators on manifolds with cusps of rank one. This includes the case of spinor Laplacians on (XX)-rank one locally symmetric spaces. The time-dependent approach to scattering theory is taken to derive the main results about the spectral resolution of these operators. The second part of the book deals with the derivation of an index formula for generalized Dirac operators on manifolds with cusps of rank one. This index formula is used to prove a conjecture of Hirzebruch concerning the relation of signature defects of cusps of Hilbert modular varieties and special values of L-series. This book is intended for readers working in the field of automorphic forms and analysis on non-compact Riemannian manifolds, and assumes a knowledge of PDE, scattering theory and harmonic analysis on semisimple Lie groups.

Keywords

Signatur Spinor derivation manifold

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0077660
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-17696-1
  • Online ISBN 978-3-540-47762-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book