Vanishing theorem for 2-torsion instanton invariants

Abstract

For any closed, oriented, simply connected spin 4-manifold $X$ with $b_{X}^{+}>1$ and even, by Fintushel and Stern [7], differential-topological polynomial invariants with its values in $Z_{2}$ are defined. These invariants are analogues of Donaldson polynomial invariants. In [7], it is proved that if $X=X^{\prime}\# S^{2}\times S^{2}$, then these invariants do not always vanish. But in this paper, it is proved that these invariants vanish for a large class of connected sums.