Heath Emerson

An Introduction to C*-Algebras and Noncommutative Geometry

• Gebundenes Buch

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.

Produktdetails

• Birkhäuser Advanced Texts Basler Lehrbücher
• Verlag: Birkhäuser / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-031-59849-4
• 2024
• Seitenzahl: 556
• Erscheinungstermin: 28. Juli 2024
• Englisch
• Abmessung: 241mm x 160mm x 36mm
• Gewicht: 936g
• ISBN-13: 9783031598494
• ISBN-10: 3031598490
• Artikelnr.: 70285226

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.