Author: Werner MüllerPublisher:
ISBN:
Category : Elliptic operators
Languages : en
Pages : 260
Book Description
L2-index of Elliptic Operators on Manifolds with Cusps of Rank One
Author: Werner MüllerPublisher:
ISBN:
Category : Elliptic operators
Languages : en
Pages : 260
Book Description
Manifolds with Cusps of Rank One
Author: Werner MüllerPublisher: Springer
ISBN: 3540477624
Category : Mathematics
Languages : en
Pages : 169
Book Description
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.
L-index L2-index of elliptic operators on manifolds with cusps of rank one
Author: Werner MüllerL_1hn2-index of elliptic operators on manifolds with cusps of rank one
Author: Werner MüllerL Hoch 2 -index of Elliptic Operators on Manifolds with Cusps of Rank One
Author: W. MuellerAutomorphic Forms and Geometry of Arithmetic Varieties
Author: K. HashimotoPublisher: Academic Press
ISBN: 1483218074
Category : Mathematics
Languages : en
Pages : 540
Book Description
Automorphic Forms and Geometry of Arithmetic Varieties deals with the dimension formulas of various automorphic forms and the geometry of arithmetic varieties. The relation between two fundamental methods of obtaining dimension formulas (for cusp forms), the Selberg trace formula and the index theorem (Riemann-Roch's theorem and the Lefschetz fixed point formula), is examined. Comprised of 18 sections, this volume begins by discussing zeta functions associated with cones and their special values, followed by an analysis of cusps on Hilbert modular varieties and values of L-functions. The reader is then introduced to the dimension formula of Siegel modular forms; the graded rings of modular forms in several variables; and Selberg-Ihara's zeta function for p-adic discrete groups. Subsequent chapters focus on zeta functions of finite graphs and representations of p-adic groups; invariants and Hodge cycles; T-complexes and Ogata's zeta zero values; and the structure of the icosahedral modular group. This book will be a useful resource for mathematicians and students of mathematics.
Geometric and Topological Invariants of Elliptic Operators
Author: Jerome KaminkerPublisher: American Mathematical Soc.
ISBN: 0821851128
Category : Mathematics
Languages : en
Pages : 312
Book Description
This volume contains the proceedings of the AMS-IMS-SIAM Summer Research Conference on ``Geometric and Topological Invariants of Elliptic Operators,'' held in August 1988 at Bowdoin College. Some of the themes covered at the conference and appearing in the articles are: the use of more sophisticated asymptotic methods to obtain index theorems, the study of the $\eta$ invariant and analytic torsion, and index theory on open manifolds and foliated manifolds. The current state of noncommutative differential geometry, as well as operator algebraic and $K$-theoretic methods, are also presented in several the articles. This book will be useful to researchers in index theory, operator algebras, foliations, and mathematical physics. Topologists and geometers are also likely to find useful the view the book provides of recent work in this area. In addition, because of the expository nature of several of the articles, it will be useful to graduate students interested in working in these areas.
The Atiyah-Patodi-Singer Index Theorem
Author: Richard MelrosePublisher: CRC Press
ISBN: 1439864608
Category : Mathematics
Languages : en
Pages : 392
Book Description
Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.
$L 2$-index of Elliptic Operators on Manifods with Cusps of Rank One
Author: W. MüllerL2-Invariants: Theory and Applications to Geometry and K-Theory
Author: Wolfgang LückPublisher: Springer Science & Business Media
ISBN: 3662046873
Category : Mathematics
Languages : en
Pages : 604
Book Description
In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.