SO(3) Monopoles, Level-One Seiberg-Witten Moduli Spaces, and Witten's Conjecture in Low Degrees

Details SO(3) Monopoles, Level-One Seiberg-Witten Moduli Spaces, and Witten's Conjecture in Low Degrees SO(3) Monopoles, Level-One Seiberg-Witten Moduli Spaces, and Witten's Conjecture in Low Degrees

2001-06-27

arxiv.org/abs/math/0106238v2

Mathematics

Differential Geometry

Minor corrections; details added. Topology and its Applications, 91 pages, to appear

Scientific paper

We prove Witten's formula relating the Donaldson and Seiberg-Witten series modulo powers of degree $c+2$, with $c=-{1/4}(7\chi+11\sigma)$, for four-manifolds obeying some mild conditions, where $\chi$ and $\sigma$ are their Euler characteristic and signature. We use the moduli space of SO(3) monopoles as a cobordism between a link of the Donaldson moduli space of anti-self-dual SO(3) connections and links of the moduli spaces of Seiberg-Witten monopoles. Gluing techniques allow us to compute contributions from Seiberg-Witten moduli spaces lying in the first (or `one-bubble') level of the Uhlenbeck compactification of the moduli space of SO(3) monopoles.

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