Heath Emerson

An Introduction to C*-Algebras and Noncommutative Geometry (eBook, PDF)

• Format: PDF

Produktbeschreibung

This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry. Moreover, it fills a gap in the literature, providing a clear and accessible account of the geometric picture of K-theory and its relation to the C*-algebraic picture. The text can be used as the basis for a graduate level or a capstone course with the goal being to bring a relative novice up to speed on the basic ideas while offering a glimpse at some of the more advanced topics of the subject. Coverage includes C*-algebra theory, K-theory, K-homology, Index theory and Connes' Noncommuntative Riemannian geometry.

Aimed at graduate level students, the book is also a valuable resource for mathematicians who wish to deepen their understanding of noncommutative geometry and algebraic K-theory. A wide range of important examples are introduced at the beginning of the book. There are lots of excellent exercises and any student working through these will benefit significantly. Prerequisites include a basic knowledge of algebra, analysis, and a bit of functional analysis. As the book progresses, a little more mathematical maturity is required as the text discusses smooth manifolds, some differential geometry and elliptic operator theory, and K-theory. The text is largely self-contained though occasionally the reader may opt to consult more specialized material to further deepen their understanding of certain details.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 539
• Erscheinungstermin: 27. Juli 2024
• Englisch
• ISBN-13: 9783031598500
• Artikelnr.: 72241927

Autorenporträt

Heath Emerson is Professor of Mathematics at the University of Victoria, British Columbia. His research interests include noncommutative geometry, equivariant K-theory, and the Baum-Connes conjecture.

Inhaltsangabe

An introduction to C*-algebras.- An Introduction to Index Theory and Noncommutative Geometry.- Spectral Theory and Representation.- Positivity, Representations, Tensor Products and Ideals in C*-algebras.- Module theory of C*-algebras.- Morita Equivalence.- Topological K-theory and Clifford Algebras.- K-theory for C*algebras.- The Index Theorem of Atiyah and Singer.- K-homology and Noncommutative Geometry.- An Introduction to KK-theory.- Bibliography.

Rezensionen

This book serves as a textbook that leads readers from a beginner's course on C*-algebra, through the Atiyah-Singer index theorem, to advanced topics in noncommutative geometry, such as cyclic cohomology and Kasparov's KK-theory. ... Each section is accompanied by a number of problems, and a notable advantage of the book is the extensive collection of examples scattered throughout the text. Some of them serve as a pretext for introducing some interesting advanced topics of noncommutative geometry. (Vladimir Manuilov, Mathematical Reviews, April, 2025)

Writing a textbook on noncommutative geometry looks like an insurmountable obstacle. The present monograph overcomes all these difficulties with great success. This type of an introductory text is overdue and indispensable to any academic library. the monograph is a solid and accessible introductory course in noncommutative geometry written for the graduate students and non-experts in the field. (Igor V. Nikolaev, zbMATH 1566.46002, 2025)

This book serves as a textbook that leads readers from a beginner's course on C_-algebra, through the Atiyah-Singer index theorem, to advanced topics in noncommutative geometry, such as cyclic cohomology and Kasparov's KK-theory. ... Each section is accompanied by a number of problems, and a notable advantage of the book is the extensive collection of examples scattered throughout the text. Some of them serve as a pretext for introducing some interesting advanced topics of noncommutative geometry. (Vladimir Manuilov, Mathematical Reviews, April, 2025)