PU(2) monopoles. II: Toplevel SeibergWitten moduli spaces and Witten's conjecture in low degrees
Abstract
In this article we complete the prooffor a broad class of fourmanifoldsof Witten's conjecture that the Donaldson and SeibergWitten series coincide, at least through terms of degree less than or equal to c2, where c is a linear combination of the Euler characteristic and signature of the fourmanifold. This article is a revision of sections 47 of an earlier version, while a revision of sections 13 of that earlier version now appear in a separate companion article (math.DG/0007190). Here, we use our computations of Chern classes for the virtual normal bundles for the SeibergWitten strata from the companion article (math.DG/0007190), a comparison of all the orientations, and the PU(2) monopole cobordism to compute pairings with the links of levelzero SeibergWitten moduli subspaces of the moduli space of PU(2) monopoles. These calculations then allow us to compute lowdegree Donaldson invariants in terms of SeibergWitten invariants and provide a partial verification of Witten's conjecture.
 Publication:

eprint arXiv:dgga/9712005
 Pub Date:
 December 1997
 DOI:
 10.48550/arXiv.dgga/9712005
 arXiv:
 arXiv:dgga/9712005
 Bibcode:
 1997dg.ga....12005F
 Keywords:

 Mathematics  Differential Geometry;
 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 Journal fur die Reine und Angewandte Mathematik, to appear