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The Seiberg-Witten equations on end-periodic manifolds and an obstruction to positive scalar curvature metrics

林剑锋 Massachusetts Institute of Technology

Geometric Analysis and Geometric Topology mathscidoc:2205.15007

Journal of topology, 12, (2), 2019.6
By studying the Seiberg-Witten equations on end-periodic manifolds, we give an obstruction on the existence of positive scalar curvature metric on compact 4-manifolds with the same homology as S1×S3. This obstruction is given in terms of the relation between the Frøyshov invariant of the generator of H3(X;Z) with the 4-dimensional Casson invariant λSW(X) defined by Mrowka-Ruberman-Saveliev. Along the way, we develop a framework that can be useful in further study of the Seiberg-Witten theory on general end-periodic manifolds.
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@inproceedings{林剑锋2019the,
  title={The Seiberg-Witten equations on end-periodic manifolds and an obstruction to positive scalar curvature metrics},
  author={林剑锋},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517175512873632252},
  booktitle={Journal of topology},
  volume={12},
  number={2},
  year={2019},
}
林剑锋. The Seiberg-Witten equations on end-periodic manifolds and an obstruction to positive scalar curvature metrics. 2019. Vol. 12. In Journal of topology. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517175512873632252.
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