An SO(3)-version of 2-torsion instanton invariants
Vol. 15 (2008), No. 2, Page 257--289.
Sasahira, Hirofumi
An SO(3)-version of 2-torsion instanton invariants
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Abstract:
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.
Mathematics Subject Classification (2000): 57R57
Mathematical Reviews Number: MR2478112
Received: 2007-01-09
