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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$K$-theory and $K$-homology relative to a $\textrm {II}_{\infty }$-factor
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by Iain Raeburn PDF
Proc. Amer. Math. Soc. 71 (1978), 294-298 Request permission

Abstract:

Let X be a compact space and M be a factor of type $\mathrm {II}_\infty$ acting on a separable Hilbert space. Let ${K_M}(X)$ denote the Grothendieck group generated by the semigroup of isomorphism classes of M-vector bundles over X, and, if X is also metric, let $\operatorname {Ext}^M(X)$ denote the group of equivalence classes of extensions of $C(X)$ relative to M. We show that ${K_M}(X)$ is the direct sum of the even-dimensional Čech cohomology groups of X, and that $\operatorname {Ext}^M(X)$ is the direct product of the odd-dimensional Čech homology groups of X.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 294-298
  • MSC: Primary 55N15; Secondary 46L99, 46M20
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0500509-4
  • MathSciNet review: 500509