EXTENSIONS OF C(X) BY SIMPLE C-ASTERISK-ALGEBRAS OF REAL RANK ZERO

Let Ext(C(X),A) be the set of unitarily equivalence classes of essenti al C-algebra extensions of the following form: 0 --> A --> E --> C(X) --> 0, where A is a nonunital separable simple C-algebra of real ran k zero, stable rank one with unique normalized trace and X is a finite CW complex. We show that there is a bijection J: 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 m ore general setting, give a condition when an essential extension is q uasidiagonal.