N = 2 topological Yang-Mills theories and Donaldson's polynomials

Abstract

The N = 2 topological Yang-Mills and holomorphic Yang-Mills theories on simply connected compact Kahler surfaces with p(g) greater than or equal to 1 are re-examined. The N = 2 symmetry is clarified in terms of a Dolbeault model of the equivariant cohomology. We realize the non-algebraic part of Donaldson's polynomial invariants as well as the algebraic part. We calculate Donaldson's polynomials on H-2,H-0(S,Z) + H-0,H-2,(S,Z).