We introduce equivalence relations among asymptotic homomorphisms that in general are stronger than homotopy, but which we show are equivalent to homotopy when the domain is a suspended C*-algebra. As an application, we show that the E-theory of Connes and Higson can be realized as a special case of Kasparov's KK-theory.
Homology, Homotopy and Applications, Vol. 8 (2006), No. 2, pp.29-49.
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