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 t...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.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11471247)the Fundamental Research Funds for the Central Universities
文摘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.
