From Differential Geometry to Non-commutative Geometry and Topology

  • Neculai S. Teleman

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Spaces, Bundles and Characteristic Classes in Differential Geometry

    1. Front Matter
      Pages 1-1
  3. Non-commutative Differential Geometry

  4. Index Theorems

    1. Front Matter
      Pages 233-233
    2. Neculai S. Teleman
      Pages 235-241
    3. Neculai S. Teleman
      Pages 243-273
    4. Neculai S. Teleman
      Pages 275-283
  5. Prospects in Index Theory

    1. Front Matter
      Pages 285-285
    2. Neculai S. Teleman
      Pages 287-328
  6. Non-commutative Topology

    1. Front Matter
      Pages 375-375
    2. Neculai S. Teleman
      Pages 377-387
  7. Back Matter
    Pages 389-398

About this book


This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.


index theory non-commutative topology non-commutative geometry Atiyah-Singer theorem global analysis

Authors and affiliations

  • Neculai S. Teleman
    • 1
  1. 1.Dipartimento di Scienze MatematicheUniversità Politecnica delle MarcheAnconaItaly

Bibliographic information