A splitting theorem for the Seiberg-Witten invariant of a homology S1×S3

林剑锋 Massachusetts Institute of Technology Daniel Ruberman Brandeis University Nikolai Saveliev University of Miami

Geometric Analysis and Geometric Topology mathscidoc:2205.15008

Geometry & Topology, 22, (5), 2018.5
We study the Seiberg-Witten invariant λSW(X) of smooth spin 4-manifolds X with integral homology of S1×S3 defined by Mrowka, Ruberman, and Saveliev as a signed count of irreducible monopoles amended by an index-theoretic correction term. We prove a splitting formula for this invariant in terms of the Frøyshov invariant h(X) and a certain Lefschetz number in the reduced monopole Floer homology of Kronheimer and Mrowka. We apply this formula to obstruct existence of metrics of positive scalar curvature on certain 4-manifolds, and to exhibit new classes of integral homology 3-spheres of Rohlin invariant one which have infinite order in the homology cobordism group.
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@inproceedings{林剑锋2018a,
  title={A splitting theorem for the Seiberg-Witten invariant of a homology S1×S3},
  author={林剑锋, Daniel Ruberman, and Nikolai Saveliev},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517175907410916253},
  booktitle={Geometry & Topology},
  volume={22},
  number={5},
  year={2018},
}
林剑锋, Daniel Ruberman, and Nikolai Saveliev. A splitting theorem for the Seiberg-Witten invariant of a homology S1×S3. 2018. Vol. 22. In Geometry & Topology. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517175907410916253.
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