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

2007/01/17 by Hirofumi Sasahira, Sasahira, H. · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0701469

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 2CP² # -CP², while it is known that any known invariant of 2CP² # -CP² coming from the Seiberg-Witten theory is trivial since 2CP² # -CP² has a positive scalar curvature metric.

Citations

• Localisation of the Donaldson's invariants along Seiberg-Witten classes

Cited by

• Steenbrink isomorphism and crystals on tubular neighbourhoods
• Toroidal compactifications and Borel--Serre compactifications

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• Floer homology for 2-torsion instanton invariants
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