## An SO(3)-version of 2-torsion instanton invariants

J. Math. Sci. Univ. Tokyo
Vol. 15 (2008), No. 2, Page 257--289.

Sasahira, Hirofumi
An SO(3)-version of 2-torsion instanton invariants
We construct an invariant for non-spin $4$-manifolds by using $2$-torsion cohomology classes of moduli spaces of instantons on $SO(3)$-bundles. The invariant is an $SO(3)$-version of Fintushel-Stern's $2$-torsion instanton invariant. We show that this $SO(3)$-torsion invariant is non-trivial for $2\CP^2 \# \barCP2$, while it is known that any known invariant of $2\CP^2 \# \barCP2$ coming from the Seiberg-Witten theory is trivial since $2\CP^2 \# \barCP2$ has a positive scalar curvature metric.