From Differential Geometry to Non-commutative Geometry and Topology
Teleman, Neculai S.
From Differential Geometry to Non-commutative Geometry and Topology [electronic resource] / by Neculai S. Teleman. - 1st ed. 2019. - XXII, 398 p. 12 illus. online resource.
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.
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.
9783030284336
10.1007/978-3-030-28433-6 doi
Differential geometry.
Manifolds (Mathematics).
Complex manifolds.
Differential Geometry.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA641-670
516.36
From Differential Geometry to Non-commutative Geometry and Topology [electronic resource] / by Neculai S. Teleman. - 1st ed. 2019. - XXII, 398 p. 12 illus. online resource.
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.
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.
9783030284336
10.1007/978-3-030-28433-6 doi
Differential geometry.
Manifolds (Mathematics).
Complex manifolds.
Differential Geometry.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA641-670
516.36