From Differential Geometry to Non-commutative Geometry and Topology

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.

Auteur

Neculai S. Teleman did his PhD with I. Singer at MIT in 1977, working on extending the index theorem to combinatorial manifolds. He was professor at the Universitá di Roma La Sapienza, at SUNY Stony Brook, and at Universitá Politechnica delle Marche, Italy. His interests are on global analysis of PL-manifolds, combinatorial Hodge Theory, Index Theory, Quasi conformal mappings, and Singularity Theory.

Contenu

1. Part I Spaces, bundles and characteristic classes in differential geometry.- 2. Part II Non-commutative differential geometry.- 3. Part III Index Theorems.- 4. Part IV Prospects in Index Theory. Part V.- 5. Non-commutative topology.