From differential geometry to non-commutative geometry and topology - Teleman, Neculai S. (Cham : Springer, 2019)
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.
Includes bibliographical reference and index.
Keywords: Geometry, Differential; Topology