Some glueing formulas for spin polynomials and a proof of the Van de Ven conjecture

Abstract

We deduce some formulas for the spin invariants of the connected sum of an arbitrary 4-manifold X, b^+ _2(X) > 0 $ with $\overline {CP^2}$ in terms of the spin invariants of $X$ and apply this to prove the Van de Ven conjecture.