Acta Mathematica Sinica, English Series

, Volume 31, Issue 6, pp 1035–1042 | Cite as

Circle action with prescribed number of fixed points



Given any two positive integers k and n, this paper is concerned with the existence of a circle action on a closed, smooth orientable n-dimensional manifold with precisely k isolated fixed points. We first show that this existence problem can be reduced to that of an n-dimensional manifold with exactly three fixed points. Then by using a rigidity result, we determine possible weights on these three fixed points when n = 4.


Circle action fixed point weight 

MR(2010) Subject Classification



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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsTongji UniversityShanghaiP. R. China

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