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C*-Algebra Extensions and K-Homology. (Am-95), Volume 95
Paperback
Series: Annals of Mathematics Studies, Book 95
ISBN13: 9780691082660
Publisher: Princeton University Press
Published: Jul 21 1980
Pages: 96
Weight: 0.41
Height: 0.34 Width: 6.06 Depth: 9.20
Language: English
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.
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