C*-Algebra Extensions and K-Homology. (AM-95), Volume 95 / Ronald G. Douglas.

Format:

Book

Author/Creator:

Douglas, Ronald G., author.

Series:

Annals of mathematics studies ; Number 95.

Annals of Mathematics Studies ; 228

Language:

English

Subjects (All):

C*-algebras.

K-theory.

Algebra, Homological.

Physical Description:

1 online resource (94 pages) : illustrations.

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X ⃗ Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained.

Contents:

Frontmatter

Contents

Preface

Chapter 1. An Overview

Chapter 2. Ext as a Group

Chapter 3. Ext as a Homotopy Functor

Chapter 4. Generalized Homology Theory and Periodicity

Chapter 5. Ext as K-Homology

Chapter 6. Index Theorems snd Novikov's Higher Signatures

References

Index

Index of Symbols

Backmatter

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400881468

1400881463

OCLC:

1024046392