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Does the suspension isomorphism $K_1(A) \to K_0(SA)$ descend from a more refined invariant?
If $A$ is a C*-algebra, denote its minimal unitization by $\tilde A$ and its suspension by $SA$, thought of as all continuous $a:[0,1] \to A$ with $a(0)=a(1)=0$. The unitized suspension $\widetilde{SA}...
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