Manifolds with Cusps of Rank One: Spectral Theory and L2-Index Theorem / Edition 1

Manifolds with Cusps of Rank One: Spectral Theory and L2-Index Theorem / Edition 1

by Werner Muller
     
 

ISBN-10: 3540176969

ISBN-13: 9783540176961

Pub. Date: 06/02/1987

Publisher: Springer Berlin Heidelberg

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…  See more details below

Overview

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.

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Product Details

ISBN-13:
9783540176961
Publisher:
Springer Berlin Heidelberg
Publication date:
06/02/1987
Series:
Lecture Notes in Mathematics Series, #1244
Edition description:
1987
Pages:
158
Product dimensions:
6.14(w) x 9.21(h) x 0.37(d)

Table of Contents

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.

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