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Local and Analytic Cyclic Homology
 
Ralf Meyer University of Göttingen, Göttingen, Germany
A publication of European Mathematical Society
Local and Analytic Cyclic Homology
Hardcover ISBN:  978-3-03719-039-5
Product Code:  EMSTM/3
List Price: $78.00
AMS Member Price: $62.40
Please note AMS points can not be used for this product
Local and Analytic Cyclic Homology
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Local and Analytic Cyclic Homology
Ralf Meyer University of Göttingen, Göttingen, Germany
A publication of European Mathematical Society
Hardcover ISBN:  978-3-03719-039-5
Product Code:  EMSTM/3
List Price: $78.00
AMS Member Price: $62.40
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS Tracts in Mathematics
    Volume: 32007; 368 pp
    MSC: Primary 19; 46

    Periodic cyclic homology is a homology theory for non-commutative algebras that plays a similar role in non-commutative geometry as de Rham cohomology for smooth manifolds. While it produces good results for algebras of smooth or polynomial functions, it fails for bigger algebras such as most Banach algebras or C*-algebras. Analytic and local cyclic homology are variants of periodic cyclic homology that work better for such algebras. In this book, the author develops and compares these theories, emphasizing their homological properties. This includes the excision theorem, invariance under passage to certain dense subalgebras, a Universal Coefficient Theorem that relates them to \(K\)-theory, and the Chern–Connes character for \(K\)-theory and \(K\)-homology.

    The cyclic homology theories studied in this text require a good deal of functional analysis in bornological vector spaces, which is supplied in the first chapters. The focal points here are the relationship with inductive systems and the functional calculus in non-commutative bornological algebras.

    Some chapters are more elementary and independent of the rest of the book and will be of interest to researchers and students working on functional analysis and its applications.

    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 local and analytic cyclic homology.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 32007; 368 pp
MSC: Primary 19; 46

Periodic cyclic homology is a homology theory for non-commutative algebras that plays a similar role in non-commutative geometry as de Rham cohomology for smooth manifolds. While it produces good results for algebras of smooth or polynomial functions, it fails for bigger algebras such as most Banach algebras or C*-algebras. Analytic and local cyclic homology are variants of periodic cyclic homology that work better for such algebras. In this book, the author develops and compares these theories, emphasizing their homological properties. This includes the excision theorem, invariance under passage to certain dense subalgebras, a Universal Coefficient Theorem that relates them to \(K\)-theory, and the Chern–Connes character for \(K\)-theory and \(K\)-homology.

The cyclic homology theories studied in this text require a good deal of functional analysis in bornological vector spaces, which is supplied in the first chapters. The focal points here are the relationship with inductive systems and the functional calculus in non-commutative bornological algebras.

Some chapters are more elementary and independent of the rest of the book and will be of interest to researchers and students working on functional analysis and its applications.

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 local and analytic cyclic homology.

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.