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Seiberg–witten equations, end-periodic dirac operators,and a lift of rohlin’s invariant

Tomasz Mrowka Massachusetts Institute of Technology Daniel Ruberman Brandeis University Nikolai Saveliev University of Miami

Differential Geometry mathscidoc:1609.10227

Journal of Differential Geometry, 88, (2), 333-377, 2011
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.
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@inproceedings{tomasz2011seiberg–witten,
  title={SEIBERG–WITTEN EQUATIONS, END-PERIODIC DIRAC OPERATORS,AND A LIFT OF ROHLIN’S INVARIANT},
  author={Tomasz Mrowka, Daniel Ruberman, and Nikolai Saveliev},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913204454138010888},
  booktitle={Journal of Differential Geometry},
  volume={88},
  number={2},
  pages={333-377},
  year={2011},
}
Tomasz Mrowka, Daniel Ruberman, and Nikolai Saveliev. SEIBERG–WITTEN EQUATIONS, END-PERIODIC DIRAC OPERATORS,AND A LIFT OF ROHLIN’S INVARIANT. 2011. Vol. 88. In Journal of Differential Geometry. pp.333-377. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913204454138010888.
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