Blow-up formulae for $SO(3)$ -Donaldson polynomials

Abstract

We calculate first through seventh order terms of a blow-up formula for $SO(3)$ -Donaldson polynomials, using equivariant cohomology and techniques similar to those of [Oz]. These formulas are used to extend the results of [B2] to any rank one negative definite four manifold and to describe the extension of the equivalence proved in [M] of the Donaldson polynomial and O'Grady's algebro-geometric analogues to t he four dimensional classes.