Advertisement

© 2001

Elements of Noncommutative Geometry

Textbook

Part of the Birkhäuser Advanced Texts book series (BAT)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Topology

    1. Front Matter
      Pages 1-1
    2. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 3-47
    3. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 49-82
    4. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 83-139
    5. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 141-167
  3. Calculus and Linear Algebra

    1. Front Matter
      Pages 169-169
    2. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 171-212
    3. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 213-250
    4. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 251-317
    5. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 319-365
  4. Geometry

    1. Front Matter
      Pages 367-367
    2. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 369-428
    3. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 429-486
    4. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 487-515
  5. Trends

    1. Front Matter
      Pages 517-517
    2. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 519-556
    3. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 557-596
    4. José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa
      Pages 597-640
  6. Back Matter
    Pages 641-685

About this book

Keywords

C*-algebra Microsoft Access algebra boundary element method clsmbc commutative property differential topology geometry knowledge language mathematics noncommutative geometry quantum field quantum field theory techniques

Authors and affiliations

  1. 1.Departamento de FísicaUniversidad de Costa RicaSan JoséCosta Rica
  2. 2.Departamento de MatemáticasUniversidad de Costa RicaSan JoséCosta Rica

Bibliographic information

Reviews

"In collecting the material in a coherent form, the authors have performed a valuable service and this book will no doubt open noncommutative geometry to a wider audience.... [A] large number of metaphorical and mathematical remarks embedded in the text...highlight the plethora of connections between the material of the book and other areas of mathematics."

Mathematical Reviews

"The material is collected from an enormous number of sources.... All of it is carefully worked out and serves as a highly recommendable introduction to the vital field of noncommutative geometry."

Zentralblatt Math

"The style of the book is lively, exempt of the stereotypes one encounters rather often in the mathematical literature. The authors know how to tell stories and enjoy doing it. The friendly tone could be of some help for an hypothetical unexperienced reader confronted with almost 700 pages of rather difficult and delicate mathematics."

—Journal of Operator Theory

"The present book is a systematic course in noncommutative differential geometry and operator theory, with applications to guantum physics.  Its topics cover C*-algebras, vector bundles and C*-modules, K-theory, Fredholm operators, Clifford algebras, Spin representations, noncommutative integration and differential calculus, spectral triples and Connes spin manifold theorem. As applications, noncommutative tori, quantum theory and Kreimer-Connes-Moscovici algebras are discussed.  The book will be helpful to all mathematicians and mathematical physicits who wish to learn about noncommutative geometry and tis ramifications."

---Matheamtica Bohemica