There is Rosenberg-Schochet universal coefficient theorem, which says $KK(A,B)\simeq Ext(K_*(A),K_{+1}(B))\oplus Hom(K_(A),K_*(B))$ Ext(K_{\ast}(A),K_{\ast+1}(B))\oplus Hom(K_{\ast}(A),K_{\ast}(B))$ (not canonically) when $A$ is $KK$-equivalent to a commutative algebra. It was proved in The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized K-functor, Duke Math. J., 55(1987), 431–474.
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There is Rosenberg-Schochet universal coefficient theorem, which says $KK(A,B)\simeq Ext(K_*(A),K_{+1}(B))\oplus Hom(K_(A),K_*(B))$ (not canonically) when $A$ is $KK$-equivalent to a commutative algebra. It was proved in The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized K-functor, Duke Math. J., 55(1987), 431–474. |
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