Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Manuilov, VladimirThomsen, Klaus2019-06-2820101864-7596https://doi.org/10.34657/3143https://oa.tib.eu/renate/handle/123456789/1727Let A, A0 be separable C*-algebras, B a stable ¾-unital C*-algebra. Our main result is the construction of the pairing [[A';A]] £ Ext¡1=2(A;B) ! Ext¡1=2(A';B), where [[A';A]] denotes the set of homotopy classes of asymptotic homomorphisms from A' to A and Ext¡1=2(A;B) is the group of semi-invertible extensions of A by B. Assume that all extensions of A by B are semi-invertible. Then this pairing allows us to give a condition on A' that provides semi-invertibility of all extensions of A' by B. This holds, in particular, if A and A' are shape equivalent. A similar condition implies that if Ext¡1=2 coincides with E-theory (via the Connes-Higson map) for A then the same holds for A'.application/pdfeng510Report