### Abstract

We introduce a gauge-theoretic integer valued lift of the Rohlin invariant of a smooth 4-manifold X with the homology of S^{1}×S^{3}. The invariant has two terms: one is a count of solutions to the Seiberg-Witten equations on X, and the other is essentially the index of the Dirac operator on a non-compact manifold with end modeled on the infinite cyclic cover of X. Each term is metric (and perturbation) dependent, and we show that these dependencies cancel as the metric and perturbation vary in a generic 1-parameter family.

Original language | English (US) |
---|---|

Pages (from-to) | 333-377 |

Number of pages | 45 |

Journal | Journal of Differential Geometry |

Volume | 88 |

Issue number | 2 |

State | Published - Jun 2011 |

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### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis
- Geometry and Topology

### Cite this

*Journal of Differential Geometry*,

*88*(2), 333-377.

**Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant.** / Mrowka, Tomasz; Ruberman, Daniel; Saveliev, Nikolai.

Research output: Contribution to journal › Article

*Journal of Differential Geometry*, vol. 88, no. 2, pp. 333-377.

}

TY - JOUR

T1 - Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant

AU - Mrowka, Tomasz

AU - Ruberman, Daniel

AU - Saveliev, Nikolai

PY - 2011/6

Y1 - 2011/6

N2 - We introduce a gauge-theoretic integer valued lift of the Rohlin invariant of a smooth 4-manifold X with the homology of S1×S3. The invariant has two terms: one is a count of solutions to the Seiberg-Witten equations on X, and the other is essentially the index of the Dirac operator on a non-compact manifold with end modeled on the infinite cyclic cover of X. Each term is metric (and perturbation) dependent, and we show that these dependencies cancel as the metric and perturbation vary in a generic 1-parameter family.

AB - We introduce a gauge-theoretic integer valued lift of the Rohlin invariant of a smooth 4-manifold X with the homology of S1×S3. The invariant has two terms: one is a count of solutions to the Seiberg-Witten equations on X, and the other is essentially the index of the Dirac operator on a non-compact manifold with end modeled on the infinite cyclic cover of X. Each term is metric (and perturbation) dependent, and we show that these dependencies cancel as the metric and perturbation vary in a generic 1-parameter family.

UR - http://www.scopus.com/inward/record.url?scp=80053493375&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053493375&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:80053493375

VL - 88

SP - 333

EP - 377

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

SN - 0022-040X

IS - 2

ER -