Extensions of C(X) by Simple C*-algebras of real rank zero

Let Ext(C(X), A) be the set of unitarily equivalence classes of essential C*-algebra extensions of the following form: 0 → A → E → C(X) → 0, where A is a nonunital separable simple C*-algebra of real rank zero, stable rank one with unique normalized trace and X is a finite CW complex. We show that there is a bijection [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]: Ext(C(X), A) → KK(C(X),M(A)/A), where M(A) is the multiplier algebra of A. In particular, we determine when an extension is actually splitting. We also, in a more general setting, give a condition when an essential extension is quasidiagonal.