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From Differential Geometry to Non-commutative Geometry and Topology de Neculai S. Teleman

From Differential Geometry to Non-commutative Geometry and Topology

Autor Neculai S. Teleman
en Limba Engleză Paperback – 18 noi 2020
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.

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Specificații

ISBN-13: 9783030284350
ISBN-10: 3030284352
Pagini: 398
Ilustrații: XXII, 398 p. 12 illus.
Dimensiuni: 155 x 235 x 26 mm
Greutate: 0.64 kg
Ediția:1st ed. 2019
Editura: Springer International Publishing
Colecția Springer
Locul publicării:Cham, Switzerland

Cuprins

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.

Recenzii

“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)

Notă biografică

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.

Textul de pe ultima copertă

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.

Caracteristici

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