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I am interested in the K-theory of the Bohr compactification $\mathbb{R}_B$ of the real numbers.

Do we have $K_0(C(\mathbb{R}_B))$ isomorphic to $K_1(C(\mathbb{R}_B))$ ?

More generally, what do we know about these groups ? Have they been determined ?

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  • $\begingroup$ What is $C(-)$? $\endgroup$ Jan 20, 2012 at 10:52
  • $\begingroup$ By $C(X)$, I mean the algebra of continuous functions from $X$ to $\mathbb{C}$. $\endgroup$
    – Oliver
    Jan 23, 2012 at 5:07

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