An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants

Book excerpt: "We prove an analogue of the Kotschick-Morgan Conjecture in the context of SO(3) monopoles, obtaining a formula relating the Donaldson and Seiberg-Witten invariants of smooth four-manifolds using the SO(3)-monopole cobordism. The main technical difficulty in the SO(3)-monopole program relating the Seiberg- Witten and Donaldson invariants has been to compute intersection pairings on links of strata of reducible SO(3) monopoles, namely the moduli spaces of Seiberg- Witten monopoles lying in lower-level strata of the Uhlenbeck compactification of the moduli space of SO(3) monopoles [...]. In this monograph, we prove -- modulo a gluing theorem which is an extension of our earlier work in PU(2) monopoles. III: Existence of gluing and obstruction maps [...] that these intersection pairings can be expressed in terms of topological data and Seiberg-Witten invariants of the four-manifold. [...]--Page xi.