QUATERNIONIC MONOPOLES

We present the simplest non-abelian version of Seiberg-Witten theory: Quaternionic monopoles. These monopoles are associated with Spin(h)(4) -structures on 4-manifolds and form finite-dimensional moduli spaces. On a Kahler surface the quaternionic monopole equations decouple and l ead to the projective vortex equation for holomorphic pairs. This vort ex equation comes from a moment map and gives rise to a new complex-ge ometric stability concept. The moduli spaces of quaternionic monopoles on Kahler surfaces have two closed subspaces, both naturally isomorph ic with moduli spaces of canonically stable holomorphic pairs. These c omponents intersect along a Donaldson instanton space and can be compa ctified with Seiberg-Witten moduli spaces. This should provide a link between the two corresponding theories.