C*-algebra Extensions and K-homology

Released on by Ronald G. Douglas
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  • C*-algebra Extensions and K-homology Book Detail

  • Author : Ronald G. Douglas
  • Release Date : 1980-07-21
  • Publisher : Princeton University Press
  • Genre : Mathematics
  • Pages : 112
  • ISBN 13 : 9780691082660
  • File Size : 30,30 MB
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C*-algebra Extensions and K-homology by Ronald G. Douglas PDF Summary

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.

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