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

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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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     author = {G. S. Makeev},
     title = {Yet {Another} {Description} of the {Connes--Higson} {Functor}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {561--574},
     publisher = {mathdoc},
     volume = {107},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_4_a6/}
}
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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/