C*-Algebra Extensions and K-Homology. (AM-95), Volume 95 PDF Download

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C*-Algebra Extensions and K-Homology. (AM-95), Volume 95

C*-Algebra Extensions and K-Homology. (AM-95), Volume 95 PDF Author: Ronald G. Douglas
Publisher: Princeton University Press
ISBN: 1400881463
Category : Mathematics
Languages : en
Pages : 96

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Book Description
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.