ENGLISH

From Differential Geometry to Non-commutative Geometry and Topology

By Neculai S. Teleman

Book information

Publisher
Springer International Publishing
Year
2019
ISBN
978-3-030-28432-9, 978-3-030-28433-6
Language
english
Format
PDF
Filesize
4 MB (4512382 bytes)
Edition
1st ed. 2019
Pages
XXII, 398\406
Time added
2020-02-08 04:41:43
Mathematics; Differential Geometry; Manifolds and

Description

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. Front Matter ....Pages i-xxi Front Matter ....Pages 1-1 Spaces, Bundles and Characteristic Classes in Differential Geometry (Neculai S. Teleman)....Pages 3-81 Front Matter ....Pages 83-83 Spaces, Bundles, Homology/Cohomology and Characteristic Classes in Non-commutative Geometry (Neculai S. Teleman)....Pages 85-168 Hochschild, Cyclic and Periodic Cyclic Homology (Neculai S. Teleman)....Pages 169-231 Front Matter ....Pages 233-233 Analytic Structures on Topological Manifolds (Neculai S. Teleman)....Pages 235-241 Index Theorems in Differential Geometry (Neculai S. Teleman)....Pages 243-273 Index Theorems in Non-commutative Geometry (Neculai S. Teleman)....Pages 275-283 Front Matter ....Pages 285-285 Algebraic Structures (Neculai S. Teleman)....Pages 287-328 Topological Index and Analytical Index: Reformulation of Index Theory (Neculai S. Teleman)....Pages 329-342 Local Hochschild Homology of the Algebra of Hilbert–Schmidt Operators on Simplicial Spaces (Neculai S. Teleman)....Pages 343-374 Front Matter ....Pages 375-375 Non-commutative Topology (Neculai S. Teleman)....Pages 377-387 Back Matter ....Pages 389-398

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