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Manifolds with Cusps of Rank One

Spectral Theory and L2-Index Theorem

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  • © 1987
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Overview

Authors:
  1. Werner Müller
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1244)

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-X
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  2. Preliminaries

    • Werner Müller
    Pages 1-4
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  3. Cusps of rank one

    • Werner Müller
    Pages 5-12
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  4. The heat equation on the cusp

    • Werner Müller
    Pages 13-21
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  5. The Neumann laplacian on the cusp

    • Werner Müller
    Pages 22-30
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  6. Manifolds with cusps of rank one

    • Werner Müller
    Pages 31-45
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  7. The spectral resolution of H

    • Werner Müller
    Pages 46-59
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  8. The heat kernel

    • Werner Müller
    Pages 60-63
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  9. The eisenstein functions

    • Werner Müller
    Pages 64-73
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  10. The spectral shift function

    • Werner Müller
    Pages 74-83
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  11. The L2-index of generalized dirac operators

    • Werner Müller
    Pages 84-99
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  12. The unipotent contribution to the index

    • Werner Müller
    Pages 100-138
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  13. The Hirzebruch conjecture

    • Werner Müller
    Pages 139-149
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  14. Back Matter

    Pages 150-158
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Manifolds with Cusps of Rank One

  • Book Subtitle: Spectral Theory and L2-Index Theorem

  • Authors: Werner Müller

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0077660

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Softcover ISBN: 978-3-540-17696-1Published: 27 March 1987

  • eBook ISBN: 978-3-540-47762-4Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 158

  • Topics: Manifolds and Cell Complexes (incl. Diff.Topology), Computer Science, general

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