PU(2) monopoles and links of top-level Seiberg-Witten moduli spaces

Details PU(2) monopoles and links of top-level Seiberg-Witten moduli spaces PU(2) monopoles and links of top-level Seiberg-Witten moduli spaces

2000-07-31

arxiv.org/abs/math/0007190v2

J. reine angew. Math. 538 (2001), 57-133

Mathematics

Differential Geometry

Journal fur die Reine und Angewandte Mathematik, to appear; 64 pages

Scientific paper

This is the first of two articles in which we give a proof - for a broad class of four-manifolds - of Witten's conjecture that the Donaldson and Seiberg-Witten series 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 of the four-manifold. This article is a revision of sections 1-3 of an earlier version of the article dg-ga/9712005, now split into two parts, while a revision of sections 4-7 of that earlier version appears in a recently updated dg-ga/9712005. In the present article, we construct virtual normal bundles for the Seiberg-Witten strata of the moduli space of PU(2) monopoles and compute their Chern classes.

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