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 2ℂℙ2#ℂℙ̄2, while it is known that any known invariant of 2ℂℙ2#ℂℙ̄2 coming from the Seiberg-Witten theory is trivial since 2ℂℙ 2#ℂℙ̄2 has a positive scalar curvature metric.
|Number of pages||33|
|Journal||Journal of Mathematical Sciences|
|Publication status||Published - Dec 1 2008|
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Applied Mathematics