COMPUTATIONS OF INSTANTON INVARIANTS USING DONALDSON-FLOER THEORY

We compute the Donaldson SU(2)-invariants of the double cover of CP2 b ranched over a smooth algebraic curve of degree eight. From this we de duce a formula for the relative invariants of the blow-up of the Gompf nucleus N2, and we show how this gives a blow-up formula for a class of 4-manifolds which includes essentially all the simply connected 4-m anifolds known to have big diffeomorphism group. We apply the result o n the nucleus also to prove a formula for the invariants of minimal si mply connected elliptic surfaces which reduces the computation to the case of geometric genus one. In particular, we compute all the Donalds on invariants of minimal simply connected elliptic surfaces without mu ltiple fibers. Our main tool is Donaldson-Floer theory.