N=2 topological Yang-Mills theory on compact Kähler surfaces

We study a topological Yang-Mills theory withN=2 fermionic symmetry. Our formalism is a field theoretical interpretation of the Donaldson polynomial invariants on compact Kähler surfaces. We also study an analogous theory on compact oriented Riemann surfaces and briefly discuss a possible application of Witten's non-Abelian localization formula to the problems in the case of compact Kähler surfaces.This article was typeset by the author using Pjour1