2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64884Let A and B be $C^*$-algebras, A separable, and B $σ$-unital and stable. It is shown that there are natural isomorphisms $E(A,B)=KK(SA,Q(B))=[SA,Q(B)\otimes K]$, where $SA=C_0(0,1)\otimes A$, $[\cdot,\cdot]$ denotes the set of homotopy classes of *-homomorphisms, $Q(B) = M(B)/B$ is the generalized Calkin algebra and K denotes the $C^*$-algebra of compact operators.22 pages, LaTeXOperator Algebrastext