  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 lead to
the projective vortex equation for holomorphic pairs. This vortex equation
comes from a moment map and gives rise to a new complex-geometric stability
concept. The moduli spaces of quaternionic monopoles on Kahler surfaces have
two closed subspaces, both naturally isomorphic with moduli spaces of
canonically stable holomorphic pairs. These components intersect along
Donaldsons instanton space and can be compactified with Seiberg-Witten moduli
spaces. This should provide a link between the two corresponding theories.
Notes: To appear in CMP The revised version contains more details concerning
the Uhlenbeck compactfication of the moduli space of quaternionic monopoles,
and possible applications are discussed. Attention ! Due to an ununderstandable
mistake, the duke server had replaced all the symbols "=" by "=3D" in the
tex-file of the revised version we sent on February, the 2-nd. The command
"\def{\ad}" had also been damaged !
