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 Kähler surfaces with p g ≥ 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 2,0 ( S, Z ) ⊕ H 0,2 ( S, Z ).