Manifolds with Cusps of Rank One

Spectral Theory and L2-Index Theorem
1987
ISBN: 978-3-540-17696-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1244, 158 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 271 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Müller, Werner

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

Preliminaries.- Cusps of rank one.- The heat equation on the cusp.- The Neumann laplacian on the cusp.- Manifolds with cusps of rank one.- The spectral resolution of H.- The heat kernel.- The eisenstein functions.- The spectral shift function.- The L2-index of generalized dirac operators.- The unipotent contribution to the index.- The Hirzebruch conjecture.