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

Format:

Book

Author/Creator:

Emerson, Heath, author.

Series:

Birkhäuser Advanced Texts Basler Lehrbücher, 2296-4894

Language:

English

Subjects (All):

K-theory.

Topology.

Geometry, Differential.

Dynamics.

Functional analysis.

K-Theory.

Differential Geometry.

Dynamical Systems.

Functional Analysis.

Local Subjects:

K-Theory.

Topology.

Differential Geometry.

Dynamical Systems.

Functional Analysis.

Physical Description:

1 online resource (548 pages)

Edition:

1st ed. 2024.

Place of Publication:

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

Summary:

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.

Contents:

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.

Notes:

Includes bibliographical references.

Other Format:

Print version: Emerson, Heath An Introduction to C*-Algebras and Noncommutative Geometry

ISBN:

9783031598500

OCLC:

1450835111