1.

Record Nr.

UNINA9910154752903321

Autore

Douglas Ronald G.

Titolo

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

Pubbl/distr/stampa

Princeton, NJ : , : Princeton University Press, , [2016]

©1980

ISBN

1-4008-8146-3

Descrizione fisica

1 online resource (94 pages) : illustrations

Collana

Annals of Mathematics Studies ; ; 228

Disciplina

512/.55

Soggetti

C*-algebras

K-theory

Algebra, Homological

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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

Sommario/riassunto

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.