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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Extending cellular cohomology to $C^ *$-algebras
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by Ruy Exel and Terry A. Loring
Trans. Amer. Math. Soc. 329 (1992), 141-160
DOI: https://doi.org/10.1090/S0002-9947-1992-1024770-7
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Abstract:

A filtration on the $K$-theory of ${C^*}$-algebras is introduced. The relative quotients define groups ${H_n}(A),n \geq 0$, for any ${C^*}$-algebra $A$, which we call the spherical homology of $A$. This extends cellular cohomology in the sense that \[ {H_n}(C(X)) \otimes {\mathbf {Q}} \cong {H^n}(X;{\mathbf {Q}})\] for $X$ a finite CW-complex. While no extension of cellular cohomology which is derived from a filtration on $K$-theory can be additive, Morita-invariant, and continuous, ${H_n}$ is shown to be infinitely additive, Morita invariant for unital ${C^*}$-algebras, and continuous in limited cases.
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Bibliographic Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 329 (1992), 141-160
  • MSC: Primary 46L80; Secondary 19K56, 46M20, 58A10, 58G12
  • DOI: https://doi.org/10.1090/S0002-9947-1992-1024770-7
  • MathSciNet review: 1024770