C Algebras And Elliptic Operators In Differential Topology
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C Algebras And Elliptic Operators In Differential Topology
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Author : I_U_ri_ Petrovich Solov_v Evgeni_ Vadimovich Troit_s_ki_
language : en
Publisher: American Mathematical Soc.
Release Date : 2000-10-03
C Algebras And Elliptic Operators In Differential Topology written by I_U_ri_ Petrovich Solov_v Evgeni_ Vadimovich Troit_s_ki_ 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 2000-10-03 with categories.
The aim of this book is to present some applications of functional analysis and the theory of differential operators to the investigation of topological invariants of manifolds. The main topological application discussed in the book concerns the problem of the description of homotopy-invariant rational Pontryagin numbers of non-simply connected manifolds and the Novikov conjecture of homotopy invariance of higher signatures. The definition of higher signatures and the formulation of the Novikov conjecture are given in Chapter 3. In this chapter, the authors also give an overview of different approaches to the proof of the Novikov conjecture. First, there is the Mishchenko symmetric signature and the generalized Hirzebruch formulae and the Mishchenko theorem of homotopy invariance of higher signatures for manifolds whose fundamental groups have a classifying space, being a complete Riemannian non-positive curvature manifold. Then the authors present Solovyov's proof of the Novikov conjecture for manifolds with fundamental group isomorphic to a discrete subgroup of a linear algebraic group over a local field, based on the notion of the Bruhat-Tits building. Finally, the authors discuss the approach due to Kasparov based on the operator $KK$-theory and another proof of the Mishchenko theorem. In Chapter 4, they outline the approach to the Novikov conjecture due to Connes and Moscovici involving cyclic homology. That allows one to prove the conjecture in the case when the fundamental group is a (Gromov) hyperbolic group. The text provides a concise exposition of some topics from functional analysis (for instance, $C^*$-Hilbert modules, $K$-theory or $C^*$-bundles, Hermitian $K$-theory, Fredholm representations, $KK$-theory, and functional integration) from the theory of differential operators (pseudodifferential calculus and Sobolev chains over $C^*$-algebras), and from differential topology (characteristic classes). The book explains basic ideas of the subject and can serve as a course text for an introduction to the study of original works and special monographs.
Elliptic Theory And Noncommutative Geometry
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Author : Vladimir E. Nazaykinskiy
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-30
Elliptic Theory And Noncommutative Geometry written by Vladimir E. Nazaykinskiy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-30 with Mathematics categories.
This comprehensive yet concise book deals with nonlocal elliptic differential operators. These are operators whose coefficients involve shifts generated by diffeomorphisms of the manifold on which the operators are defined. This is the first book featuring a consistent application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators. To make the book self-contained, the authors have included necessary geometric material.
Hilbert C Modules
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Author : Vladimir Markovich Manuĭlov
language : en
Publisher: American Mathematical Soc.
Release Date :
Hilbert C Modules written by Vladimir Markovich Manuĭlov 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 with Mathematics categories.
Based on lectures delivered by the authors at Moscow State University, this volume presents a detailed introduction to the theory of Hilbert $C*$-modules. Hilbert $C*$-modules provide a natural generalization of Hilbert spaces arising when the field of scalars $\mathbf{C $ is replaced by an arbitrary $C*$-algebra. The general theory of Hilbert $C*$-modules appeared more than 30 years ago in the pioneering papers of W. Paschke and M. Rieffel and has proved to be a powerful tool inoperator algebras theory, index theory of elliptic operators, $K$- and $KK$-theory, and in noncommutative geometry as a whole. Alongside these applications, the theory of Hilbert $C*$-modules is interesting on its own. In this book, the authors explain in detail the basic notions and results of thetheory, and provide a number of important examples. Some results related to the authors' research interests are also included. A large part of the book is devoted to structural results (self-duality, reflexivity) and to nonadjointable operators. Most of the book can be read with only a basic knowledge of functional analysis; however, some experience in the theory of operator algebras makes reading easier.
C Algebras And Elliptic Operators In Differential Topology
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Author : IUrii Petrovich Solov'ev
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
C Algebras And Elliptic Operators In Differential Topology written by IUrii Petrovich Solov'ev 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 2001 with Mathematics categories.
The aim of this book is to present some applications of functional analysis and the theory of differential operators to the investigation of topological invariants of manifolds. The main topological application discussed in the book concerns the problem of the description of homotopy - invariant rational Pontryagin numbers of non-simply connected manifolds and the Novikov conjecture of homotopy invariance of higher signatures. The definition of higher signatures and the formulation of the Novikov conjecture are given in Chapter 3. In this chapter, the authors also give an overview of different approaches to the proof of the Novikov conjecture. First, there is the Mishchenko symmetric signature and the generalized Hirzebruch formulae and the Mishchenko theorem of homotopy invariance of higher signatures for manifolds whose fundamental groups have a classifying space, being a complete Riemannian non-positive curvature manifold.Then the authors present Solovyov's proof of the Novikov conjecture for manifolds with fundamental group isomorphic to a discrete subgroup of a linear algebraic group over a local field, based on the notion of the Bruhat-Tits building. Finally, the authors discuss the approach due to Kasparov based on the operator $KK$-theory and another proof of the Mishchenko theorem. In Chapter 4, they outline the approach to the Novikov conjecture due to Connes and Moscovici involving cyclic homology.That allows one to prove the conjecture in the case when the fundamental group is a (Gromov) hyperbolic group. The text provides a concise exposition of some topics from functional analysis (for instance, $C^*$-Hilbert modules, $K$-theory or $C^*$-bundles, Hermitian $K$-theory, Fredholm representations, $KK$-theory, and functional integration) from the theory of differential operators (pseudodifferential calculus and Sobolev chains over $C^*$-algebras), and from differential topology (characteristic classes). The book explains basic ideas of the subject and can serve as a course text for an introduction to the study of original works and special monographs.
Geometry Topology And Operator Algebras
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Author : Alexander Cardona
language : en
Publisher: Springer Nature
Release Date : 2025-04-28
Geometry Topology And Operator Algebras written by Alexander Cardona and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-28 with Science categories.
This book offers a comprehensive exploration of contemporary intersections between geometry, topology, and theoretical physics, emphasizing their mathematical foundations and applications. Originating from lectures presented by experts during two summer schools held in Villa de Leyva, Colombia, the book reflects the synergy between global analysis, operator algebras, and their role in modern physics. The chapters present state-of-the-art developments on a wide range of topics: the geometry and topology of foliations, affine manifolds, C*-algebras, and the pseudo-differential calculus of boundary value problems. These are enriched by applications to the theory of topological quantum matter. The book is suitable for graduate students and researchers, offering detailed introductions to advanced topics such as the longitudinal index theorem for foliations, the geometry of the Poincaré half-space in a C*-algebra, and mathematical frameworks for topological matter. With a balance of foundational material and novel insights, it serves as both a learning resource and a reference for advanced studies at the intersection of mathematics and physics.
C Algebras And Elliptic Theory
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Author : Bogdan Bojarski
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-09
C Algebras And Elliptic Theory written by Bogdan Bojarski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-09 with Mathematics categories.
This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of manifolds, operator and equivariant K-theory, Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others, and applications in mathematical physics. The wide spectrum of subjects reflects the diverse directions of research for which the starting point was the Atiyah-Singer index theorem.
Operator Theory Operator Algebras And Their Interactions With Geometry And Topology
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Author : Raul E Curto
language : en
Publisher: Springer Nature
Release Date : 2020-12-12
Operator Theory Operator Algebras And Their Interactions With Geometry And Topology written by Raul E Curto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-12 with Mathematics categories.
This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.
Mathematics Of Information And Coding
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Author : Te Sun Han
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Mathematics Of Information And Coding written by Te Sun Han 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 2002 with Computers categories.
This book is intended to provide engineering and/or statistics students, communications engineers, and mathematicians with the firm theoretic basis of source coding (or data compression) in information theory. Although information theory consists of two main areas, source coding and channel coding, the authors choose here to focus only on source coding. The reason is that, in a sense, it is more basic than channel coding, and also because of recent achievements in source coding and compression. An important feature of the book is that whenever possible, the authors describe universal coding methods, i.e., the methods that can be used without prior knowledge of the statistical properties of the data. The authors approach the subject of source coding from the very basics to the top frontiers in an intuitively transparent, but mathematically sound, manner. The book serves as a theoretical reference for communication professionals and statisticians specializing in information theory. It will also serve as an excellent introductory text for advanced-level and graduate students taking elementary or advanced courses in telecommunications, electrical engineering, statistics, mathematics, and computer science.
C Algebras And Elliptic Operators In Differential Topology
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Author : I︠U︡. P. (I︠U︡riĭ Petrovich) Solovʹëv
language : en
Publisher:
Release Date : 2001
C Algebras And Elliptic Operators In Differential Topology written by I︠U︡. P. (I︠U︡riĭ Petrovich) Solovʹëv and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
Infinite Dimensional Lie Algebras
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Author : Minoru Wakimoto
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Infinite Dimensional Lie Algebras written by Minoru Wakimoto 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 2001 with Mathematics categories.
This volume begins with an introduction to the structure of finite-dimensional simple Lie algebras, including the representation of ${\widehat {\mathfrak {sl}}}(2, {\mathbb C})$, root systems, the Cartan matrix, and a Dynkin diagram of a finite-dimensional simple Lie algebra. Continuing on, the main subjects of the book are the structure (real and imaginary root systems) of and the character formula for Kac-Moody superalgebras, which is explained in a very general setting. Only elementary linear algebra and group theory are assumed. Also covered is modular property and asymptotic behavior of integrable characters of affine Lie algebras. The exposition is self-contained and includes examples. The book can be used in a graduate-level course on the topic.