From Differential Geometry to Non-commutative Geometry and Topology

• Main Author: Teleman, Neculai S. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Subjects: Differential geometry.; Manifolds (Mathematics).; Complex manifolds.; Differential Geometry.; Manifolds and Cell Complexes (incl. Diff.Topology).
• Physical Description: XXII, 398 p. 12 illus. online resource.
• ISBN: 9783030284336
• DOI: 10.1007/978-3-030-28433-6

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.