  In this paper we identify QD(A,B), the quasidiagonal classes in KK_1(A,B), in
terms of K_*(A) and K_*(B), and we use these results in various applications.
Here is our central result.
  Theorem: Suppose that A is in the category of separable nuclear C^*-algebras
which satisfy the UCT and A is quasidiagonal relative to B. Then there is a
natural isomorphism QD(A,B) = Pext (K_*(A), K_*(B))_0 .
  Thus quasidiagonality of KK-classes is indeed a topological invariant. We
give several applications. Finally, we establish a converse to a theorem of
Davidson, Herrero, and Salinas, giving conditions under which the
quasidiagonality of A/K implies the quasidiagonality of the associated
representation of A.
