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

Original language | English |
---|---|

Pages (from-to) | 257-289 |

Number of pages | 33 |

Journal | Journal of Mathematical Sciences |

Volume | 15 |

Issue number | 2 |

Publication status | Published - Dec 1 2008 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Journal of Mathematical Sciences*,

*15*(2), 257-289.

**An SO(3)-version of 2-torsion instanton invariants.** / Sasahira, Hirofumi.

Research output: Contribution to journal › Article

*Journal of Mathematical Sciences*, vol. 15, no. 2, pp. 257-289.

}

TY - JOUR

T1 - An SO(3)-version of 2-torsion instanton invariants

AU - Sasahira, Hirofumi

PY - 2008/12/1

Y1 - 2008/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77957825427&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957825427&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77957825427

VL - 15

SP - 257

EP - 289

JO - Journal of Mathematical Sciences (Japan)

JF - Journal of Mathematical Sciences (Japan)

SN - 1340-5705

IS - 2

ER -