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

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 $2CP^2 # -CP^2$, while it is known that any known invariant of $2CP^2 # -CP^2$ coming from the Seiberg-Witten theory is trivial since $2CP^2 # -CP^2$ has a positive scalar curvature metric.

References in corpus (3)

• Localisation of the Donaldson's invariants along Seiberg-Witten classes
• PU(2) monopoles and links of top-level Seiberg-Witten moduli spaces
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Cited by in corpus (6)

• Logarithmic Geometry and Moduli
• Round handles, logarithmic transforms, and smooth 4-manifolds
• Instanton Floer homology for lens spaces
• Steenbrink isomorphism and crystals on tubular neighbourhoods
• Toroidal compactifications and Borel--Serre compactifications
• Geometric polarized log Hodge structures with a base of log rank one