Some remarks on circle action on manifolds

Ping Li Kefeng Liu

Algebraic Topology and General Topology mathscidoc:1912.43070

arXiv preprint arXiv:1008.4826, 2010.8
This paper contains several results concerning circle action on almost-complex and smooth manifolds. More precisely, we show that, for an almost-complex manifold M^{2mn} (resp. a smooth manifold M^{2mn} ), if there exists a partition M^{2mn} of weight M^{2mn} such that the Chern number M^{2mn} (resp. Pontrjagin number M^{2mn} ) is nonzero, then\emph {any} circle action on M^{2mn} (resp. M^{2mn} ) has at least M^{2mn} fixed points. When an even-dimensional smooth manifold M^{2mn} admits a semi-free action with isolated fixed points, we show that M^{2mn} bounds, which generalizes a well-known fact in the free case. We also provide a topological obstruction, in terms of the first Chern class, to the existence of semi-free circle action with\emph {nonempty} isolated fixed points on almost-complex manifolds. The main ingredients of our proofs are Bott's residue formula and rigidity theorem.
No keywords uploaded!
[ Download ] [ 2019-12-21 11:13:54 uploaded by Kefeng_Liu ] [ 220 downloads ] [ 0 comments ]
@inproceedings{ping2010some,
  title={Some remarks on circle action on manifolds},
  author={Ping Li, and Kefeng Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111354945802630},
  booktitle={arXiv preprint arXiv:1008.4826},
  year={2010},
}
Ping Li, and Kefeng Liu. Some remarks on circle action on manifolds. 2010. In arXiv preprint arXiv:1008.4826. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111354945802630.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved