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Operator Algebras and Geometry
 
Hitoshi Moriyoshi Keio University, Yokohama, Japan
Toshikazu Natsume Nagoya Institute of Technology, Nagoya, Japan
Front Cover for Operator Algebras and Geometry
Available Formats:
Hardcover ISBN: 978-0-8218-3947-8
Product Code: MMONO/237
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
Electronic ISBN: 978-1-4704-1623-2
Product Code: MMONO/237.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $58.40
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  • Front Cover for Operator Algebras and Geometry
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Operator Algebras and Geometry
Hitoshi Moriyoshi Keio University, Yokohama, Japan
Toshikazu Natsume Nagoya Institute of Technology, Nagoya, Japan
Available Formats:
Hardcover ISBN:  978-0-8218-3947-8
Product Code:  MMONO/237
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
Electronic ISBN:  978-1-4704-1623-2
Product Code:  MMONO/237.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $58.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $117.00
MAA Member Price: $105.30
AMS Member Price: $93.60
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 2372008; 155 pp
    MSC: Primary 46;

    In the early 1980's topologists and geometers for the first time came across unfamiliar words like \(C^*\)-algebras and von Neumann algebras through the discovery of new knot invariants (by V. F. R. Jones) or through a remarkable result on the relationship between characteristic classes of foliations and the types of certain von Neumann algebras. During the following two decades, a great deal of progress was achieved in studying the interaction between geometry and analysis, in particular in noncommutative geometry and mathematical physics. The present book provides an overview of operator algebra theory and an introduction to basic tools used in noncommutative geometry. The book concludes with applications of operator algebras to Atiyah–Singer type index theorems. The purpose of the book is to convey an outline and general idea of operator algebra theory, to some extent focusing on examples.

    The book is aimed at researchers and graduate students working in differential topology, differential geometry, and global analysis who are interested in learning about operator algebras.

    Readership

    Graduate students and research mathematicians interested in applications of functional analysis to geometry and topology.

  • Table of Contents
     
     
    • Chapters
    • $C^*$-algebras
    • $K$-theory
    • $KK$-theory
    • Von Neumann algebras
    • Cyclic cohomology
    • Quantizations and index theory
    • Foliation index theorems
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Volume: 2372008; 155 pp
MSC: Primary 46;

In the early 1980's topologists and geometers for the first time came across unfamiliar words like \(C^*\)-algebras and von Neumann algebras through the discovery of new knot invariants (by V. F. R. Jones) or through a remarkable result on the relationship between characteristic classes of foliations and the types of certain von Neumann algebras. During the following two decades, a great deal of progress was achieved in studying the interaction between geometry and analysis, in particular in noncommutative geometry and mathematical physics. The present book provides an overview of operator algebra theory and an introduction to basic tools used in noncommutative geometry. The book concludes with applications of operator algebras to Atiyah–Singer type index theorems. The purpose of the book is to convey an outline and general idea of operator algebra theory, to some extent focusing on examples.

The book is aimed at researchers and graduate students working in differential topology, differential geometry, and global analysis who are interested in learning about operator algebras.

Readership

Graduate students and research mathematicians interested in applications of functional analysis to geometry and topology.

  • Chapters
  • $C^*$-algebras
  • $K$-theory
  • $KK$-theory
  • Von Neumann algebras
  • Cyclic cohomology
  • Quantizations and index theory
  • Foliation index theorems
Please select which format for which you are requesting permissions.