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Circle action and some vanishing results on manifolds

Ping Li Kefeng Liu

Algebraic Topology and General Topology mathscidoc:1912.43084

International Journal of Mathematics, 22, (11), 1603-1610, 2011.11
Kawakubo and Uchida showed that, if a closed oriented 4k-dimensional manifold M admits a semi-free circle action such that the dimension of the fixed point set is less than 2k, then the signature of M vanishes. In this note, by using G-signature theorem and the rigidity of the signature operator, we generalize this result to more general circle actions. Combining the same idea with the remarkable WittenTaubesBott rigidity theorem, we explore more vanishing results on spin manifolds admitting such circle actions. Our results are closely related to some earlier results of ConnerFloyd, LandweberStong and HirzebruchSlodowy.
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@inproceedings{ping2011circle,
  title={Circle action and some vanishing results on manifolds},
  author={Ping Li, and Kefeng Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111442688626644},
  booktitle={International Journal of Mathematics},
  volume={22},
  number={11},
  pages={1603-1610},
  year={2011},
}
Ping Li, and Kefeng Liu. Circle action and some vanishing results on manifolds. 2011. Vol. 22. In International Journal of Mathematics. pp.1603-1610. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111442688626644.
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