Overview
Compiles all the tools and results of index theory, so the reader obtains a good overview of the topic
Shows that the index formula is a topological statement, giving the reader a new perspective on index theory
Presents detailed steps of non-trivial computations, which enables the reader to achieve them
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Table of contents (10 chapters)
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Front Matter
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Spaces, Bundles and Characteristic Classes in Differential Geometry
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Front Matter
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Non-commutative Differential Geometry
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Front Matter
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Non-commutative Topology
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“The present book is well written. It is very useful to researchers in differential geometry who are interested in non-commutative geometry. It provides motivations for tudying non commutative geometry.” (Ion Mihai, zbMATH 1458.58001, 2021)
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: From Differential Geometry to Non-commutative Geometry and Topology
Authors: Neculai S. Teleman
DOI: https://doi.org/10.1007/978-3-030-28433-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-28432-9Published: 18 November 2019
Softcover ISBN: 978-3-030-28435-0Published: 18 November 2020
eBook ISBN: 978-3-030-28433-6Published: 10 November 2019
Edition Number: 1
Number of Pages: XXII, 398
Number of Illustrations: 12 b/w illustrations
Topics: Differential Geometry, Manifolds and Cell Complexes (incl. Diff.Topology)