Manifolds With Cusps Of Rank One
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Manifolds With Cusps Of Rank One
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Author : Werner Müller
language : en
Publisher: Springer
Release Date : 2006-11-15
Manifolds With Cusps Of Rank One written by Werner Müller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.
Manifolds With Cusps Of Rank One
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Author : Werner Müller
language : en
Publisher:
Release Date : 1987
Manifolds With Cusps Of Rank One written by Werner Müller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Differential operators categories.
Manifolds With Cusps Of Rank One
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Author : Werner Muller
language : en
Publisher:
Release Date : 2014-09-01
Manifolds With Cusps Of Rank One written by Werner Muller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
L2 Index Of Elliptic Operators On Manifolds With Cusps Of Rank One
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Author : Werner Müller
language : en
Publisher:
Release Date : 1985
L2 Index Of Elliptic Operators On Manifolds With Cusps Of Rank One written by Werner Müller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Elliptic operators categories.
Global Analysis On Open Manifolds
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Author : Jürgen Eichhorn
language : en
Publisher: Nova Publishers
Release Date : 2007
Global Analysis On Open Manifolds written by Jürgen Eichhorn and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Global analysis is the analysis on manifolds. Since the middle of the sixties there exists a highly elaborated setting if the underlying manifold is compact, evidence of which can be found in index theory, spectral geometry, the theory of harmonic maps, many applications to mathematical physics on closed manifolds like gauge theory, Seiberg-Witten theory, etc. If the underlying manifold is open, i.e. non-compact and without boundary, then most of the foundations and of the great achievements fail. Elliptic operators are no longer Fredholm, the analytical and topological indexes are not defined, the spectrum of self-adjoint elliptic operators is no longer discrete, functional spaces strongly depend on the operators involved and the data from geometry, many embedding and module structure theorems do not hold, manifolds of maps are not defined, etc. It is the goal of this new book to provide serious foundations for global analysis on open manifolds, to discuss the difficulties and special features which come from the openness and to establish many results and applications on this basis.
Geometric And Topological Invariants Of Elliptic Operators
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Author : Jerome Kaminker
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Geometric And Topological Invariants Of Elliptic Operators written by Jerome Kaminker and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
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.
Relative Index Theory Determinants And Torsion For Open Manifolds
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Author : Jrgen Eichhorn
language : en
Publisher: World Scientific
Release Date : 2009
Relative Index Theory Determinants And Torsion For Open Manifolds written by Jrgen Eichhorn and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators. On open manifolds, nearly all of this fails, with the exception of some special classes. The goal of this monograph is to establish for open manifolds, structures and differential operators an applicable theory of number-valued relative invariants. This is of great use in the theory of moduli spaces for nonlinear partial differential equations and mathematical physics. The book is self-contained: in particular, it contains an outline of the necessary tools from nonlinear Sobolev analysis.
Handbook Of Teichm Ller Theory
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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2007
Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The Teichmuller space of a surface was introduced by O. Teichmuller in the 1930s. It is a basic tool in the study of Riemann's moduli spaces and the mapping class groups. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. The original setting of Teichmuller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmuller space and its asymptotic geometry. Teichmuller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group $G$, most notably $G=\mathrm{PSL}(2,\mathbb{R})$ and $G=\mathrm{PSL}(2,\mathbb{C})$. In the 1980s, there evolved an essentially combinatorial treatment of the Teichmuller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmuller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmuller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are self-contained and have a pedagogical character. They are written by leading experts in the subject.
Hyperbolic Manifolds
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Author : Albert Marden
language : en
Publisher: Cambridge University Press
Release Date : 2016-02
Hyperbolic Manifolds written by Albert Marden and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02 with Mathematics categories.
This study of hyperbolic geometry has both pedagogy and research in mind, and includes exercises and further reading for each chapter.
Automorphic Forms And Geometry Of Arithmetic Varieties
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Author : K. Hashimoto
language : en
Publisher: Academic Press
Release Date : 2014-07-14
Automorphic Forms And Geometry Of Arithmetic Varieties written by K. Hashimoto and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
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.