Elements of Noncommutative Geometry

ISBN: 978-1-4612-6569-6 (Print) 978-1-4612-0005-5 (Online)

Table of contents (14 chapters)

  1. Front Matter

    Pages i-xvii

  2. Topology

    1. Front Matter

      Pages 1-1

    2. No Access

      Chapter

      Pages 3-47

      Noncommutative Topology: Spaces

    3. No Access

      Chapter

      Pages 49-82

      Noncommutative Topology: Vector Bundles

    4. No Access

      Chapter

      Pages 83-139

      Some Aspects of K-theory

    5. No Access

      Chapter

      Pages 141-167

      Fredholm Operators on C*-modules

  3. Calculus and Linear Algebra

    1. Front Matter

      Pages 169-169

    2. No Access

      Chapter

      Pages 171-212

      Finite-dimensional Clifford Algebras and Spinors

    3. No Access

      Chapter

      Pages 213-250

      The Spin Representation

    4. No Access

      Chapter

      Pages 251-317

      The Noncommutative Integral

    5. No Access

      Chapter

      Pages 319-365

      Noncommutative Differential Calculi

  4. Geometry

    1. Front Matter

      Pages 367-367

    2. No Access

      Chapter

      Pages 369-428

      Commutative Geometries

    3. No Access

      Chapter

      Pages 429-486

      Spectral Triples

    4. No Access

      Chapter

      Pages 487-515

      Connes’ Spin Manifold Theorem

  5. Trends

    1. Front Matter

      Pages 517-517

    2. No Access

      Chapter

      Pages 519-556

      Tori

    3. No Access

      Chapter

      Pages 557-596

      Quantum Theory

    4. No Access

      Chapter

      Pages 597-640

      Kreimer-Connes-Moscovici Algebras

  6. Back Matter

    Pages 641-685