1.

Record Nr.

UNINA9910878058803321

Autore

Emerson Heath

Titolo

An Introduction to C-Algebras and Noncommutative Geometry / / by Heath Emerson

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2024

ISBN

9783031598500

9783031598494

Edizione

[1st ed. 2024.]

Descrizione fisica

1 online resource (548 pages)

Collana

Birkhäuser Advanced Texts Basler Lehrbücher, , 2296-4894

Disciplina

512.55

Soggetti

K-theory

Topology

Geometry, Differential

Dynamics

Functional analysis

K-Theory

Differential Geometry

Dynamical Systems

Functional Analysis

C*-àlgebres

Geometria diferencial no commutativa

Teoria espectral (Matemàtica)

K-teoria

Teoria de l'índex (Matemàtica)

Llibres electrònics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

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.

Sommario/riassunto

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.