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K-Theory and Noncommutative Geometry
 
Edited by: Guillermo Cortiñas University of Buenos Aires, Buenos Aires, Argentina
Joachim Cuntz University of Münster, Munster, Germany
Max Karoubi Université Paris VII, Paris, France
Ryszard Nest University of Copenhagen, Copenhagen, Denmark
Charles A. Weibel Rutgers University, New Brunswick, NJ
A publication of European Mathematical Society
K-Theory and Noncommutative Geometry
Hardcover ISBN:  978-3-03719-060-9
Product Code:  EMSSCR/2
List Price: $124.00
AMS Member Price: $99.20
Please note AMS points can not be used for this product
K-Theory and Noncommutative Geometry
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K-Theory and Noncommutative Geometry
Edited by: Guillermo Cortiñas University of Buenos Aires, Buenos Aires, Argentina
Joachim Cuntz University of Münster, Munster, Germany
Max Karoubi Université Paris VII, Paris, France
Ryszard Nest University of Copenhagen, Copenhagen, Denmark
Charles A. Weibel Rutgers University, New Brunswick, NJ
A publication of European Mathematical Society
Hardcover ISBN:  978-3-03719-060-9
Product Code:  EMSSCR/2
List Price: $124.00
AMS Member Price: $99.20
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS Series of Congress Reports
    Volume: 22008; 454 pp
    MSC: Primary 19; 58; 14; 46; 53;

    Since its inception 50 years ago, K-theory has been a tool for understanding a wide-ranging 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 K-theory 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 K-theory, 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 K-theory. There are primary and secondary Chern characters which pass from K-theory 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 K-theory, noncommmutative geometry, and other branches of mathematics.

    A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

    Readership

    Graduate students and research mathematicians interested in K-theory and noncommutative geometry.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 22008; 454 pp
MSC: Primary 19; 58; 14; 46; 53;

Since its inception 50 years ago, K-theory has been a tool for understanding a wide-ranging 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 K-theory 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 K-theory, 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 K-theory. There are primary and secondary Chern characters which pass from K-theory 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 K-theory, noncommmutative geometry, and other branches of mathematics.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in K-theory and noncommutative geometry.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.