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The Connes-Higson construction is an isomorphism | V. Manuilov
; K. Thomsen
; | Date: |
28 Apr 2000 | Subject: | Operator Algebras | math.OA | Affiliation: | Moscow State U.) and K. Thomsen (Aarhus U. | Abstract: | Let $A$ be a separable $C^*$-algebra and $B$ a stable $C^*$-algebra containing a strictly positive element. We show that the group $Ext(SA,B)$ of unitary equivalence classes of extensions of $SA$ by $B$, modulo the extensions which are asymptotically split, coincides with the group of homotopy classes of such extensions. This is done by proving that the Connes-Higson construction gives rise to an isomorphism between $Ext(SA,B)$ and the $E$-theory group $E(A,B)$ of homotopy classes of asymptotic homomorphisms from $S^2A$ to $B$. | Source: | arXiv, math.OA/0004181 | Services: | Forum | Review | PDF | Favorites |
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