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

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Douglas, Ronald G.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2016]; ©1980
• Year of Publication: 2016
• Language: English
• Series: Annals of Mathematics Studies ; 95
• Physical Description: 1 online resource (96 p.)
• Other title: 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400881468; 9783110494914; 9783110442496
• DOI: 10.1515/9781400881468
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Ronald G. Douglas.

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.