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In this article we complete the proof---for a broad class offour-manifolds---of Witten's conjecture that the Donaldson and Seiberg-Wittenseries coincide, at least through terms of degree less than or equal to c-2,where c is a linear combination of the Euler characteristic and signature ofthe four-manifold. This article is a revision of sections 4--7 of an earlierversion, while a revision of sections 1--3 of that earlier version now appearin a separate companion article (math.DG/0007190). Here, we use ourcomputations of Chern classes for the virtual normal bundles for theSeiberg-Witten strata from the companion article (math.DG/0007190), acomparison of all the orientations, and the PU(2) monopole cobordism to computepairings with the links of level-zero Seiberg-Witten moduli subspaces of themoduli space of PU(2) monopoles. These calculations then allow us to computelow-degree Donaldson invariants in terms of Seiberg-Witten invariants andprovide a partial verification of Witten's conjecture.Comment: Journal fur die Reine und Angewandte Mathematik, to appear; 65 pages.  Revision of sections 4-7 of version v1 (December 1997

PU (2) monopoles. II: Top-level Seiberg-Witten moduli spaces and Witten's conjecture in low degrees