Geodesic
Yet Another Description of the Connes--Higson Functor
Matematičeskie zametki, Tome 107 (2020) no. 4, pp. 561-574.

Voir la notice de l'article provenant de la source Math-Net.Ru

Suppose that $A$ and $B$ are $C^{*}$-algebras, $A$ is separable, and $B$ is stable. The elements of the group $E_{1}(A,B)$ in Connes–Higson $E$-theory are represented by $*$-homomorphisms from the suspension of $A$ to the asymptotic algebra $\mathfrak AB$. In the paper, an endofunctor $\mathfrak M$ in the category of $C^{*}$-algebras is constructed and a set of special homotopy classes of $*$-homomorphisms from $A$ to $\mathfrak{MA}B$ is defined so that this set endowed with the natural structure of an Abelian group coincides with $E_{1}(A,B)$.
Keywords: $E$-theory, $KK$-theory, homotopy invariant functor. 
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G. S. Makeev. Yet Another Description of the Connes--Higson Functor. Matematičeskie zametki, Tome 107 (2020) no. 4, pp. 561-574. http://geodesic.mathdoc.fr/item/MZM_2020_107_4_a6/

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