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 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.

Original languageEnglish
Pages (from-to)257-289
Number of pages33
JournalJournal of Mathematical Sciences
Volume15
Issue number2
Publication statusPublished - Dec 1 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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