Joachim Cuntz's Books

Noncommutative Geometry

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000

By: Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts

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Noncommutative Geometry

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000

By: Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts

Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

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364

Publisher

Springer

Published Date

ISBN 10

3540397027

ISBN 13

9783540397021

Topological and Bivariant K-Theory

By: Joachim Cuntz,Jonathan Rosenberg

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Topological and Bivariant K-Theory

By: Joachim Cuntz,Jonathan Rosenberg

Topological K-theory is one of the most important invariants for noncommutative algebras. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. This book describes a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, it details other approaches to bivariant K-theories for operator algebras. The book studies a number of applications, including K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.

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268

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Springer Science & Business Media

Published Date

ISBN 10

3764383984

ISBN 13

9783764383985

Cyclic Homology in Non-Commutative Geometry

By: Joachim Cuntz,Georges Skandalis,Boris Tsygan

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Cyclic Homology in Non-Commutative Geometry

By: Joachim Cuntz,Georges Skandalis,Boris Tsygan

Contributions by three authors treat aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different points of view. The connections between (bivariant) K-theory and cyclic theory via generalized Chern-characters are discussed in detail. Cyclic theory is the natural setting for a variety of general abstract index theorems. A survey of such index theorems is given and the concepts and ideas involved in these theorems are explained.

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147

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Springer Science & Business Media

Published Date

ISBN 10

3662064448

ISBN 13

9783662064443

K-Theory for Group C-Algebras and Semigroup C-Algebras

By: Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu

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K-Theory for Group C-Algebras and Semigroup C-Algebras

By: Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu

This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions. Part of the most basic structural information for such a C*-algebra is contained in its K-theory. The determination of the K-groups of C*-algebras constructed from group or semigroup actions is a particularly challenging problem. Paul Baum and Alain Connes proposed a formula for the K-theory of the reduced crossed product for a group action that would permit, in principle, its computation. By work of many hands, the formula has by now been verified for very large classes of groups and this work has led to the development of a host of new techniques. An important ingredient is Kasparov's bivariant K-theory. More recently, also the C*-algebras generated by the regular representation of a semigroup as well as the crossed products for actions of semigroups by endomorphisms have been studied in more detail. Intriguing examples of actions of such semigroups come from ergodic theory as well as from algebraic number theory. The computation of the K-theory of the corresponding crossed products needs new techniques. In cases of interest the K-theory of the algebras reflects ergodic theoretic or number theoretic properties of the action.

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325

Publisher

Birkhäuser

Published Date

ISBN 10

3319599151

ISBN 13

9783319599151

Basic Bundle Theory and K-Cohomology Invariants

By: Dale Husemöller,Michael Joachim,Branislav Jurco,Martin Schottenloher

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Basic Bundle Theory and K-Cohomology Invariants

By: Dale Husemöller,Michael Joachim,Branislav Jurco,Martin Schottenloher

Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory. It aims to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object. One renewed motivation for studying this subject, comes from quantum field theory, where topological invariants play an important role.

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344

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Springer

Published Date

ISBN 10

354074956X

ISBN 13

9783540749561

Continuous Tensor Products and Arveson's Spectral $C^*$-Algebras

By: Joachim Zacharias

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Continuous Tensor Products and Arveson's Spectral $C^*$-Algebras

By: Joachim Zacharias

This book is intended for graduate students and research mathematicians interested in operator algebras

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Page Count

135

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821815458

ISBN 13

9780821815458

Stability of Spherically Symmetric Wave Maps

By: Joachim Krieger

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Stability of Spherically Symmetric Wave Maps

By: Joachim Krieger

Presents a study of Wave Maps from ${\mathbf{R}}^{2+1}$ to the hyperbolic plane ${\mathbf{H}}^{2}$ with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some $H^{1+\mu}$, $\mu>0$.

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American Mathematical Soc.

Published Date

ISBN 10

0821838776

ISBN 13

9780821838778

Pseudo-Differential Operators

Quantization and Signals

By: Hans G. Feichtinger,Bernard Helffer,Michael Lamoureux,Nicolas Lerner,Joachim Toft

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Pseudo-Differential Operators

Quantization and Signals

By: Hans G. Feichtinger,Bernard Helffer,Michael Lamoureux,Nicolas Lerner,Joachim Toft

Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.

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235

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Springer

Published Date

ISBN 10

3540682686

ISBN 13

9783540682684

K-Theory for Group C-Algebras and Semigroup C-Algebras

By: Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu

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K-Theory for Group C-Algebras and Semigroup C-Algebras

By: Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu

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Page Count

325

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Birkhäuser

Published Date

ISBN 10

3319599151

ISBN 13

9783319599151

Noncommutative Geometry

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000

By: Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts

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Noncommutative Geometry

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000

By: Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts

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Page Count

364

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Springer

Published Date

ISBN 10

3540397027

ISBN 13

9783540397021

Cyclic Cohomology and Noncommutative Geometry

By: Joachim J. R. Cuntz,Masoud Khalkhali

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Cyclic Cohomology and Noncommutative Geometry

By: Joachim J. R. Cuntz,Masoud Khalkhali

Noncommutative geometry is a new field that is among the great challenges of present-day mathematics. Its methods allow one to treat noncommutative algebras - such as algebras of pseudodifferential operators, group algebras, or algebras arising from quantum field theory - on the same footing as commutative algebras, that is, as spaces. Applications range over many fields of mathematics and mathematical physics. This volume contains the proceedings of the workshop on "Cyclic Cohomology and Noncommutative Geometry" held at the Fields Institute in June 1995.

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199

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821808230

ISBN 13

9780821808238

Cyclic Homology in Non-Commutative Geometry

By: Joachim Cuntz,Georges Skandalis,Boris Tsygan

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Cyclic Homology in Non-Commutative Geometry

By: Joachim Cuntz,Georges Skandalis,Boris Tsygan

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160

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540404694

ISBN 13

9783540404699

Topological and Bivariant K-Theory

By: Joachim Cuntz,Jonathan Rosenberg

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Topological and Bivariant K-Theory

By: Joachim Cuntz,Jonathan Rosenberg

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268

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3764383984

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9783764383985

Book's by Joachim Cuntz

Noncommutative Geometry

Noncommutative Geometry

Topological and Bivariant K-Theory

Topological and Bivariant K-Theory

Cyclic Homology in Non-Commutative Geometry

Cyclic Homology in Non-Commutative Geometry

K-Theory for Group C-Algebras and Semigroup C-Algebras

K-Theory for Group C-Algebras and Semigroup C-Algebras

Basic Bundle Theory and K-Cohomology Invariants

Basic Bundle Theory and K-Cohomology Invariants

Continuous Tensor Products and Arveson's Spectral $C^*$-Algebras

Continuous Tensor Products and Arveson's Spectral $C^*$-Algebras

Stability of Spherically Symmetric Wave Maps

Stability of Spherically Symmetric Wave Maps

Pseudo-Differential Operators

Pseudo-Differential Operators

K-Theory for Group C-Algebras and Semigroup C-Algebras

K-Theory for Group C-Algebras and Semigroup C-Algebras

Noncommutative Geometry

Noncommutative Geometry

Cyclic Cohomology and Noncommutative Geometry

Cyclic Cohomology and Noncommutative Geometry

Cyclic Homology in Non-Commutative Geometry

Cyclic Homology in Non-Commutative Geometry

Topological and Bivariant K-Theory

Topological and Bivariant K-Theory

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