Cuntz, Joachim J. R. 1948
Overview
Works:  46 works in 71 publications in 2 languages and 633 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Thesis advisor 
Classifications:  QA564, 516.35 
Publication Timeline
.
Most widely held works by
Joachim J. R Cuntz
Cyclic homology in noncommutative geometry by
Joachim J. R Cuntz(
Book
)
4 editions published in 2004 in English and held by 229 WorldCat member libraries worldwide
This volume contains contributions by three authors and treats aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different and complementary points of view. The connections between topological (bivariant) Ktheory and cyclic theory via generalized Cherncharacters are discussed in detail. This includes an outline of a framework for bivariant Ktheory on a category of locally convex algebras. On the other hand, cyclic theory is the natural setting for a variety of general index theorems. A survey of such index theorems (including the abstract index theorems of ConnesMoscovici and of BresslerNestTsygan) is given and the concepts and ideas involved in the proof of these theorems are explained
4 editions published in 2004 in English and held by 229 WorldCat member libraries worldwide
This volume contains contributions by three authors and treats aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different and complementary points of view. The connections between topological (bivariant) Ktheory and cyclic theory via generalized Cherncharacters are discussed in detail. This includes an outline of a framework for bivariant Ktheory on a category of locally convex algebras. On the other hand, cyclic theory is the natural setting for a variety of general index theorems. A survey of such index theorems (including the abstract index theorems of ConnesMoscovici and of BresslerNestTsygan) is given and the concepts and ideas involved in the proof of these theorems are explained
Cyclic cohomology and noncommutative geometry(
Book
)
8 editions published between 1997 and 1998 in English and held by 166 WorldCat member libraries worldwide
Noncommutative geometry is a new field that is among the great challenges of presentday 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 (Waterloo, ON) in June 1995. The workshop was part of the program for the special year on operator algebras and its applications
8 editions published between 1997 and 1998 in English and held by 166 WorldCat member libraries worldwide
Noncommutative geometry is a new field that is among the great challenges of presentday 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 (Waterloo, ON) in June 1995. The workshop was part of the program for the special year on operator algebras and its applications
C*algebras : proceedings of the SFBWorkshop on C*Algebras, Münster, Germany, March 812, 1999 by
Joachim Cuntz(
Book
)
3 editions published in 2000 in English and held by 140 WorldCat member libraries worldwide
This book represents the refereed proceedings of the SFBWorkshop on C*Algebras which was held at Münster in March 1999. It contains articles by some of the best researchers on the subject of C*algebras about recent developments in the field of C*algebra theory and its connections to harmonic analysis and noncommutative geometry. Among the contributions there are several excellent surveys and overviews and some original articles covering areas like the classification of C*algebras, Ktheory, exact C*algebras and exact groups, CuntzKriegerPimsner algebras, group C*algebras, the BaumConnes conjecture and others
3 editions published in 2000 in English and held by 140 WorldCat member libraries worldwide
This book represents the refereed proceedings of the SFBWorkshop on C*Algebras which was held at Münster in March 1999. It contains articles by some of the best researchers on the subject of C*algebras about recent developments in the field of C*algebra theory and its connections to harmonic analysis and noncommutative geometry. Among the contributions there are several excellent surveys and overviews and some original articles covering areas like the classification of C*algebras, Ktheory, exact C*algebras and exact groups, CuntzKriegerPimsner algebras, group C*algebras, the BaumConnes conjecture and others
Lokale Eigenschaften von Operatoralgebren by
Joachim J. R Cuntz(
Book
)
3 editions published in 1975 in English and German and held by 13 WorldCat member libraries worldwide
3 editions published in 1975 in English and German and held by 13 WorldCat member libraries worldwide
Topological and bivariant Ktheory by
Joachim Cuntz(
Book
)
2 editions published in 2007 in English and held by 12 WorldCat member libraries worldwide
Topological Ktheory is one of the most important invariants for noncommutative algebras equipped with a suitable topology or bornology. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic Ktheory. We describe a bivariant Ktheory for bornological algebras, which provides a vast generalization of topological Ktheory. In addition, we discuss other approaches to bivariant Ktheories for operator algebras. As applications, we study Ktheory of crossed products, the BaumConnes assembly map, twisted Ktheory with some of its applications, and some variants of the AtiyahSinger Index Theorem
2 editions published in 2007 in English and held by 12 WorldCat member libraries worldwide
Topological Ktheory is one of the most important invariants for noncommutative algebras equipped with a suitable topology or bornology. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic Ktheory. We describe a bivariant Ktheory for bornological algebras, which provides a vast generalization of topological Ktheory. In addition, we discuss other approaches to bivariant Ktheories for operator algebras. As applications, we study Ktheory of crossed products, the BaumConnes assembly map, twisted Ktheory with some of its applications, and some variants of the AtiyahSinger Index Theorem
Operator algebras and noncommutative geometry(
Book
)
4 editions published in 2005 in English and held by 8 WorldCat member libraries worldwide
4 editions published in 2005 in English and held by 8 WorldCat member libraries worldwide
Operator algebras and noncommutative geometry(
Book
)
in English and held by 4 WorldCat member libraries worldwide
in English and held by 4 WorldCat member libraries worldwide
Operator algebras and noncommutative geometry(
Book
)
2 editions published in 2002 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2002 in English and held by 4 WorldCat member libraries worldwide
Simple C*algebras generated by isometries II by
Joachim J. R Cuntz(
Book
)
2 editions published in 1977 in German and held by 2 WorldCat member libraries worldwide
2 editions published in 1977 in German and held by 2 WorldCat member libraries worldwide
Operator algebras and mathematical physics : conference proceedings : Constanța (Romania), July 27, 2001 by (
Book
)
2 editions published in 2003 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2003 in English and held by 2 WorldCat member libraries worldwide
Operator algebras and noncommutative geometry. Classification of nuclear C@*algebras, Entropy in operator algebras(
Book
)
1 edition published in 2002 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 2 WorldCat member libraries worldwide
C *  Algebren : 6.  12.2.94(
Book
)
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
The structure of multiplication and addition in simple c*algebras by
Joachim J. R Cuntz(
Book
)
2 editions published in 1976 in Undetermined and English and held by 2 WorldCat member libraries worldwide
2 editions published in 1976 in Undetermined and English and held by 2 WorldCat member libraries worldwide
Topological markov chains with dicyclic dimension groups by
Joachim J. R Cuntz(
Book
)
2 editions published in 1979 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1979 in English and held by 2 WorldCat member libraries worldwide
Operator algebras and noncommutative geometry. Theory of operator algebras 3(
Book
)
1 edition published in 2003 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2003 in English and held by 2 WorldCat member libraries worldwide
A characterization of algebraically simple C*algebras by
Bruce Blackadar(
Book
)
2 editions published in 1980 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1980 in English and held by 2 WorldCat member libraries worldwide
Operator algebras and noncommutative geometry. Theory of operator algebras 2(
Book
)
1 edition published in 2003 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2003 in English and held by 2 WorldCat member libraries worldwide
Dimension functions on simple C*algebras by
Joachim J. R Cuntz(
Book
)
2 editions published in 1977 in Undetermined and English and held by 2 WorldCat member libraries worldwide
2 editions published in 1977 in Undetermined and English and held by 2 WorldCat member libraries worldwide
Ktheory and noncommutative geometry by International Conference on KTheory and Noncommutative Geometry(
)
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
Since its inception 50 years ago, Ktheory has been a tool for understanding a wideranging family of mathematical structures and their invariants: topological spaces, rings, algebraic varieties and operator algebras are the dominant examples. The invariants range from characteristic classes in cohomology, determinants of matrices, Chow groups of varieties, as well as traces and indices of elliptic operators. Thus Ktheory is notable for its connections with other branches of mathematics. Noncommutative geometry develops tools which allow one to think of noncommutative algebras in the same footing as commutative ones: as algebras of functions on (noncommutative) spaces. The algebras in question come from problems in various areas of mathematics and mathematical physics; typical examples include algebras of pseudodifferential operators, group algebras, and other algebras arising from quantum field theory. To study noncommutative geometric problems one considers invariants of the relevant noncommutative algebras. These invariants include algebraic and topological Ktheory, and also cyclic homology, discovered independently by Alain Connes and Boris Tsygan, which can be regarded both as a noncommutative version of de Rham cohomology and as an additive version of Ktheory. There are primary and secondary Chern characters which pass from Ktheory to cyclic homology. These characters are relevant both to noncommutative and commutative problems, and have applications ranging from index theorems to the detection of singularities of commutative algebraic varieties. The contributions to this volume represent this range of connections between Ktheory, noncommmutative geometry, and other branches of mathematics
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
Since its inception 50 years ago, Ktheory has been a tool for understanding a wideranging family of mathematical structures and their invariants: topological spaces, rings, algebraic varieties and operator algebras are the dominant examples. The invariants range from characteristic classes in cohomology, determinants of matrices, Chow groups of varieties, as well as traces and indices of elliptic operators. Thus Ktheory is notable for its connections with other branches of mathematics. Noncommutative geometry develops tools which allow one to think of noncommutative algebras in the same footing as commutative ones: as algebras of functions on (noncommutative) spaces. The algebras in question come from problems in various areas of mathematics and mathematical physics; typical examples include algebras of pseudodifferential operators, group algebras, and other algebras arising from quantum field theory. To study noncommutative geometric problems one considers invariants of the relevant noncommutative algebras. These invariants include algebraic and topological Ktheory, and also cyclic homology, discovered independently by Alain Connes and Boris Tsygan, which can be regarded both as a noncommutative version of de Rham cohomology and as an additive version of Ktheory. There are primary and secondary Chern characters which pass from Ktheory to cyclic homology. These characters are relevant both to noncommutative and commutative problems, and have applications ranging from index theorems to the detection of singularities of commutative algebraic varieties. The contributions to this volume represent this range of connections between Ktheory, noncommmutative geometry, and other branches of mathematics
Noncommutative geometry by
Alain Connes(
)
1 edition published in 2004 in English and held by 0 WorldCat member libraries worldwide
Noncommutative Geometry is one of the most deep and vital research subjects of presentday Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, KTheory, 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
1 edition published in 2004 in English and held by 0 WorldCat member libraries worldwide
Noncommutative Geometry is one of the most deep and vital research subjects of presentday Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, KTheory, 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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Algebra Algebraic topology C*algebras Functional analysis Geometry Geometry, Algebraic Geometry, Differential Global analysis (Mathematics) Homology theory Index theorems Ktheory Mathematical physics Mathematics Noncommutative algebras Noncommutative differential geometry Noncommutative rings Operator algebras Operator theory Quantum theory Von Neumann algebras
Alternative Names
Cuntz Joachim
Cuntz, Joachim J.
Cuntz, Joachim J. R.
Cuntz, Joachim J. R. 1948
Joachim Cuntz deutscher Mathematiker, Hochschullehrer
Joachim Cuntz Duits wiskundige
Joachim Cuntz German mathematician primary author of Cuntz Algebra
Joachim Cuntz tysk matematikar
Joachim Cuntz tysk matematiker
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